Center of Mass

126 questions · Physics · JEE Main

Center of Mass

126 questions · Physics · JEE Main

Consider two blocks A and B of masses $m_{1} = 10 kg$ and $m_{2} = 5 kg$ that are placed on a frictionless table. The block A moves with a constant speed $v = 3 m / s$ towards the block B kept at rest.… Includes diagram2025 · 3 Apr · Shift 2 · Q54 · MCQ
A rod of length 5 L is bent right angle keeping one side length as 2 L . The position of the centre of mass of the system : (Consider $L = 10 cm$ ) Includes diagram2025 · 7 Apr · Shift 1 · Q54 · MCQ
Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of…2025 · 23 Jan · Shift 1 · Q62 · MCQ
The center of mass of a thin rectangular plate (fig - x ) with sides of length $a$ and $b$ , whose mass per unit area $(σ)$ varies as $σ = \frac{σ _{0} x}{ab}$ (where $σ_{0}$ is a constant), would be . Includes diagram2025 · 28 Jan · Shift 1 · Q54 · MCQ
As shown below, bob A of a pendulum having massless string of length 'R' is released from 60° to the vertical. It hits another bob B of half the mass that is at rest on a frictionless table in the center. Assuming elastic collision, the… Includes diagram2025 · 29 Jan · Shift 1 · Q66 · MCQ
Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side a in free space. At $t = 0$ , they are given an initial velocity $V_{A} = V_{0} A C, V_{B} = V_{0} B A$ … Includes diagram2025 · 29 Jan · Shift 2 · Q51 · MCQ
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_{A} = 5 m / s, v_{B} = 2 m / s, v_{C} = 4 m / s$ … Includes diagram2025 · 29 Jan · Shift 2 · Q70 · MCQ
Three identical spheres each of mass $2 M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 m$ each. Taking point of intersection of these two sides as origin, the…2024 · 1 Feb · Shift 1 · Q88 · Numerical
In a system two particles of masses $m_{1} = 3 kg$ and $m_{2} = 2 kg$ are placed at certain distance from each other. The particle of mass $m_{1}$ is moved towards the center of mass of the system through a distance $2 cm$ …2024 · 4 Apr · Shift 2 · Q81 · Numerical
A stationary particle breaks into two parts of masses $m_{A}$ and $m_{B}$ which move with velocities $v_{A}$ and $v_{B}$ respectively. The ratio of their kinetic energies $(K_{B} : K_{A})$ is :2024 · 8 Apr · Shift 1 · Q61 · MCQ
A uniform thin metal plate of mass $10 kg$ with dimensions is shown. The ratio of $x$ and y coordinates of center of mass of plate in $\frac{n}{9}$ . The value of $n$ is . Includes diagram2024 · 8 Apr · Shift 1 · Q86 · Numerical
Two bodies of mass $4 g$ and $25 g$ are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :2024 · 27 Jan · Shift 1 · Q69 · MCQ
A body of mass $1000 kg$ is moving horizontally with a velocity $6 m / s$ . If $200 kg$ extra mass is added, the final velocity (in $m / s$ ) is:2024 · 27 Jan · Shift 1 · Q75 · MCQ
A spherical body of mass $100 g$ is dropped from a height of $10 m$ from the ground. After hitting the ground, the body rebounds to a height of $5 m$ . The impulse of force imparted by the ground to the body is…2024 · 30 Jan · Shift 1 · Q78 · MCQ
An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:2024 · 31 Jan · Shift 1 · Q66 · MCQ
A solid circular disc of mass $50 kg$ rolls along a horizontal floor so that its center of mass has a speed of $0.4 m / s$ . The absolute value of work done on the disc to stop it is J.2024 · 31 Jan · Shift 1 · Q81 · Numerical
A body starts falling freely from height $H$ hits an inclined plane in its path at height $h$ . As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{H}{h}$ for which…2024 · 31 Jan · Shift 1 · Q85 · Numerical
The momentum of a body is increased by $50%$ . The percentage increase in the kinetic energy of the body is $%$ .2023 · 8 Apr · Shift 1 · Q70 · Numerical
A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity2023 · 10 Apr · Shift 1 · Q65 · MCQ
An average force of $125 N$ is applied on a machine gun firing bullets each of mass $10 g$ at the speed of $250 m / s$ to keep it in position. The number of bullets fired per second by the machine gun…2023 · 11 Apr · Shift 1 · Q60 · MCQ
A bullet of $10 g$ leaves the barrel of gun with a velocity of $600 m / s$ . If the barrel of gun is $50 cm$ long and mass of gun is $3 kg$ , then value of impulse supplied to the gun will be :2023 · 13 Apr · Shift 1 · Q46 · MCQ
A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before…2023 · 25 Jan · Shift 2 · Q72 · Numerical
As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball… Includes diagram2023 · 30 Jan · Shift 1 · Q46 · MCQ
The figure represents the momentum time ( $p - t$ ) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum… Includes diagram2023 · 30 Jan · Shift 1 · Q53 · MCQ
A ball of mass $200 g$ rests on a vertical post of height $20 m$ . A bullet of mass $10 g$ , travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball…2023 · 30 Jan · Shift 1 · Q56 · MCQ
A machine gun of mass $10 kg$ fires $20 g$ bullets at the rate of 180 bullets per minute with a speed of $100 m s^{- 1}$ each. The recoil velocity of the gun is2023 · 30 Jan · Shift 2 · Q50 · MCQ
100 balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $t s$ . The total force exerted by the balls on the wall is2023 · 31 Jan · Shift 1 · Q57 · MCQ
A ball is dropped from a height of $20 m$ . If the coefficient of restitution for the collision between ball and floor is $0.5$ , after hitting the floor, the ball rebounds to a height of $m$ .2023 · 31 Jan · Shift 2 · Q70 · Numerical
Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms $-$ 1 collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?2022 · 25 Jul · Shift 2 · Q48 · MCQ
Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of…2022 · 25 Jul · Shift 2 · Q64 · Numerical
A ball of mass $0.15 kg$ hits the wall with its initial speed of $12 ms^{- 1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $100 N$ ,…2022 · 26 Jul · Shift 2 · Q42 · MCQ
A body of mass $8 kg$ and another of mass $2 kg$ are moving with equal kinetic energy. The ratio of their respective momentum will be :2022 · 26 Jul · Shift 2 · Q43 · MCQ
An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?2022 · 26 Jun · Shift 1 · Q44 · MCQ
A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms $-$ 1. The impulse imparted to the ball is Ns.2022 · 26 Jun · Shift 2 · Q65 · Numerical
A body of mass $10 kg$ is projected at an angle of $4 5^{\circ}$ with the horizontal. The trajectory of the body is observed to pass through a point $(20, 10)$ . If $T$ is the time of flight, then its momentum vector, at…2022 · 27 Jul · Shift 2 · Q42 · MCQ
Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance…2022 · 27 Jun · Shift 1 · Q46 · MCQ
What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)2022 · 27 Jun · Shift 1 · Q49 · MCQ
In two different experiments, an object of mass $5 kg$ moving with a speed of $25 ms^{- 1}$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of…2022 · 28 Jul · Shift 1 · Q49 · MCQ
The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $ρ = ρ_{0} (1 - \frac{x ^{2}}{L ^{2}}) kg / m$ and length L (in meter) is $\frac{3 L}{α} m$ . The value…2022 · 28 Jul · Shift 2 · Q58 · Numerical
A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms $-$ 1. The velocity of the running man was ms $-$ 1,…2022 · 28 Jun · Shift 1 · Q65 · Numerical
Two bodies of mass $1 kg$ and $3 kg$ have position vectors $\hat{i} + 2 \hat{j} + \hat{k}$ and $- 3 \hat{i} - 2 \hat{j} + \hat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar…2022 · 29 Jul · Shift 1 · Q53 · MCQ
If momentum of a body is increased by 20%, then its kinetic energy increases by2022 · 29 Jul · Shift 2 · Q57 · MCQ
A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms $-$ 1 and 40 ms $-$ 1 respectively. The velocity of the third piece will…2022 · 29 Jun · Shift 1 · Q43 · MCQ
Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :2022 · 30 Jun · Shift 1 · Q48 · MCQ
Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be : Includes diagram2021 · 16 Mar · Shift 1 · Q50 · MCQ
A ball of mass 10 kg moving with a velocity $103$ m s $-$ 1 along X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of… Includes diagram2021 · 16 Mar · Shift 1 · Q69 · Numerical
A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical… Includes diagram2021 · 16 Mar · Shift 2 · Q50 · MCQ
Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed v along the line joining A and B… Includes diagram2021 · 17 Mar · Shift 2 · Q58 · MCQ
The disc of mass M with uniform surface mass density $σ$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $\frac{x}{3} \frac{a}{π}, \frac{x}{3} \frac{a}{π}$ where x is … Includes diagram2021 · 17 Mar · Shift 2 · Q62 · Numerical
A ball of mass 10 kg moving with a velocity 10 $3$ m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One… Includes diagram2021 · 18 Mar · Shift 1 · Q68 · Numerical
An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2 : m1 is :2021 · 18 Mar · Shift 2 · Q46 · MCQ
The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the particle is $52$ ms-1 and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points… Includes diagram2021 · 18 Mar · Shift 2 · Q67 · Numerical
A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is…2021 · 20 Jul · Shift 1 · Q70 · Numerical
If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :2021 · 20 Jul · Shift 2 · Q46 · MCQ
A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms $-$ 1, the impulse imparted to the gun and velocity of recoil of gun are :2021 · 22 Jul · Shift 2 · Q56 · MCQ
The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $(0, \frac{x R}{π})$ . Then, the…2021 · 22 Jul · Shift 2 · Q70 · Numerical
A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30 $^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is x…2021 · 24 Feb · Shift 1 · Q64 · Numerical
A circular hole of radius $(\frac{a}{2})$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be : Includes diagram2021 · 24 Feb · Shift 2 · Q57 · MCQ
Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B will be $\frac{A}{1}$ , so the value of A will be .2021 · 24 Feb · Shift 2 · Q64 · Numerical
Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be .2021 · 25 Feb · Shift 2 · Q75 · Numerical
Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and… Includes diagram2021 · 25 Jul · Shift 1 · Q56 · MCQ
A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial peed. The speed of the two body centre of mass is $\frac{x}{10}$ …2021 · 25 Jul · Shift 1 · Q62 · Numerical
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm'…2021 · 26 Feb · Shift 1 · Q59 · MCQ
A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = … Includes diagram2021 · 27 Aug · Shift 2 · Q63 · Numerical
Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B… Includes diagram2021 · 27 Jul · Shift 1 · Q52 · MCQ
A body of mass M moving at speed V0 collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles $θ$ 1 and $θ$ 2 with respect to the initial direction of motion of the body of mass M. The…2021 · 31 Aug · Shift 1 · Q51 · MCQ
A particle of mass m with an initial velocity $u i$ collides perfectly elastically with a mass 3 m at rest. It moves with a velocity $v j$ after collision, then, v is given by :2020 · 2 Sep · Shift 1 · Q42 · MCQ
A square shaped hole of side l = $\frac{a}{2}$ is carved out at a distance d = $\frac{a}{2}$ from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion form O is $- {a \over… Includes diagram2020 · 2 Sep · Shift 2 · Q63 · Numerical
A particle of mass m is moving along the x-axis with initial velocity $u i$ . It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If $sin θ_{1} = n sin θ_{2}$ … Includes diagram2020 · 2 Sep · Shift 2 · Q64 · Numerical
A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making… Includes diagram2020 · 3 Sep · Shift 1 · Q51 · MCQ
A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then…2020 · 3 Sep · Shift 2 · Q55 · MCQ
Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent… Includes diagram2020 · 4 Sep · Shift 1 · Q41 · MCQ
Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle…2020 · 6 Sep · Shift 1 · Q41 · Numerical
Particle A of mass m1 moving with velocity $(3 i + j) m s^{- 1}$ collides with another particle B of mass m2 which is at rest initially. Let $V_{1}$ and $V_{2}$ be…2020 · 6 Sep · Shift 2 · Q47 · MCQ
The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then value of x is .2020 · 6 Sep · Shift 2 · Q51 · Numerical
Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point: Includes diagram2020 · 7 Jan · Shift 1 · Q66 · MCQ
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are : Includes diagram2020 · 8 Jan · Shift 1 · Q42 · MCQ
A body A, of mass m = 0.1 kg has an initial velocity of 3 $i$ ms-1 . It collides elastically with another body, B of the same mass which has an initial velocity of 5 $j$ ms-1. After collision, A moves with a velocity $v = 4 (i + j)$ …2020 · 8 Jan · Shift 1 · Q51 · Numerical
A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $2 g h$ . If they collide head-on completely…2020 · 8 Jan · Shift 2 · Q44 · MCQ
As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can… Includes diagram2020 · 8 Jan · Shift 2 · Q55 · MCQ
Two particles of equal mass m have respective initial velocities $u i$ and $u (\frac{i + j}{2})$ . They collide completely inelastically. The energy lost in the process is :2020 · 9 Jan · Shift 1 · Q55 · MCQ
A particle of mass m is projected with a speed u from the ground at an angle $θ = \frac{π}{3}$ w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the…2020 · 9 Jan · Shift 2 · Q55 · MCQ
A rod of length L has non-uniform linear mass density given by $ρ$ (x) = $a + b (\frac{x}{L})^{2}$ , where a and b are constants and 0 $\leq$ x $\leq$ L. The value of x for the centre of mass of the rod is at :2020 · 9 Jan · Shift 2 · Q63 · MCQ
If 1022 gas molecules each of mass 10–26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104 m/s, the pressure exerted by the gas molecules will be of the order of :2019 · 8 Apr · Shift 1 · Q47 · MCQ
Four particles A, B, C and D with masses mA = m, mB = 2m, mC = 3m and mD = 4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is : Includes diagram2019 · 8 Apr · Shift 1 · Q73 · MCQ
A body of mass m1 moving with an unknown velocity of $v_{1} i \land$ , undergoes a collinear collision with a body of mass m2 moving with a velocity $v_{2} i \land$ . After collision, m1 and m2 move with…2019 · 8 Apr · Shift 2 · Q56 · MCQ
A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :- Includes diagram2019 · 8 Apr · Shift 2 · Q62 · MCQ
A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is :2019 · 9 Apr · Shift 1 · Q58 · MCQ
A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body ?2019 · 9 Apr · Shift 1 · Q67 · MCQ
A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the…2019 · 9 Apr · Shift 2 · Q49 · MCQ
A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass…2019 · 9 Apr · Shift 2 · Q51 · MCQ
Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M, Block A is given an initial speed $υ$ towards B due to which it collides with B perfectly… Includes diagram2019 · 9 Jan · Shift 1 · Q53 · MCQ
Two masses m and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k, at the centre of mass of the rod-mass system(see figure). Because of torsional… Includes diagram2019 · 9 Jan · Shift 1 · Q56 · MCQ
Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds u1 and u2, respectively. The values of u1… Includes diagram2019 · 10 Apr · Shift 1 · Q63 · MCQ
A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood.…2019 · 10 Jan · Shift 1 · Q56 · MCQ
A body of mass 1 kg falls freely from a height of 100 m, on a platform mass 3 kg which is mounted on a spring having spring constant k = 1.25 $\times$ 106 N/m. The body sticks to the platform and the spring's maximum compression is found…2019 · 11 Jan · Shift 1 · Q50 · MCQ
A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a…2019 · 11 Jan · Shift 2 · Q57 · MCQ
A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ms–1 with respect to the man. The speed of the man with respect to…2019 · 12 Apr · Shift 1 · Q70 · MCQ
Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be : Includes diagram2019 · 12 Apr · Shift 2 · Q63 · MCQ
A simple pendulum, made of a string of length $ℓ$ and a bob of mass m, is released from a small angle $θ_{0}$ . It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It…2019 · 12 Jan · Shift 1 · Q55 · MCQ
The position vector of the centre of mass $r_{c m}$ of an asymmetric uniform bar of negligible area of crosssection as shown in figure is : Includes diagram2019 · 12 Jan · Shift 1 · Q59 · MCQ
An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is2019 · 12 Jan · Shift 2 · Q51 · MCQ
A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90o with respect to each other. The mass of unknown particle is :2018 · 15 Apr · Shift 2 · Q65 · MCQ
The mass of a hydrogen molecule is 3.32 $\times$ 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on…2018 · Shift 0 · Q57 · MCQ
In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between…2018 · Shift 0 · Q64 · MCQ
Two particles A and B of equal mass M are moving with the same speed $υ$ as shown in the figure. They collide completely inelastically and move as a single particle C. The angle $θ$ that the path of C makes with the X-axis is… Includes diagram2017 · 9 Apr · Shift 1 · Q51 · MCQ
In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then $\frac{B C}{A B}$ is close to : Includes diagram2016 · 10 Apr · Shift 1 · Q45 · MCQ
A neutron moving with a speed ‘v’ makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is :2016 · 10 Apr · Shift 1 · Q50 · MCQ
Distance of the center of mass of a solid uniform cone from its vertex is $z_{0}$ . If the radius of its base is $R$ and its height is $h$ then $z_{0}$ is equal to :2015 · Shift 0 · Q67 · MCQ
A particle of mass $m$ moving in the $x$ direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ direction with speed $v .$ If the collision is perfectly inelastic, the percentage loss in the energy during the…2015 · Shift 0 · Q68 · MCQ
This question has statement $I$ and statement $I I$ . Of the four choices given after the statements, choose the one that best describes the two statements. Statement - $I$ : A point particle of mass $m$ moving with…2013 · Shift 0 · Q73 · MCQ
The figure shows the position $-$ time $(x - t)$ graph of one-dimensional motion of body of mass $0.4 k g .$ The magnitude of each impulse is Includes diagram2010 · Shift 0 · Q63 · MCQ
Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement - 2 : Principle of conservation of momentum holds true for all kinds of collisions.2010 · Shift 0 · Q74 · MCQ
A thin rod of length $^{'} L^{'}$ is lying along the $x$ -axis with its ends at $x = 0$ and $x = L$ . Its linear density (mass/length) varies with $x$ as $k (\frac{x}{L})^{n},$ where $n$ can be zero or any positive number. If the…2008 · Shift 0 · Q78 · MCQ
A block of mass $0.50 k g$ is moving with a speed of $2.00 m s^{- 1}$ on a smooth surface. It strike another mass of $1.0 k g$ and then they move together as a single body. The energy loss during the collision is :2008 · Shift 0 · Q85 · MCQ
A circular disc of radius $R$ is removed from a bigger circular disc of radius $2 R$ such that the circumferences of the discs coincide. The center of mass of the new disc is $α R$ form the center of the bigger disc. The value of $α$ …2007 · Shift 0 · Q96 · MCQ
A player caught a cricket ball of mass $150 g$ moving at a rate of $20 m / s .$ If the catching process is completed in $0.1 s,$ the force of the blow exerted by the ball on the hand of the player is equal to2006 · Shift 0 · Q126 · MCQ
A bomb of mass $16 k g$ at rest explodes into two pieces of masses $4 k g$ and $12 k g .$ The velocity of the $12 k g$ mass is $4 m s^{- 1} .$ The kinetic energy of the other mass is2006 · Shift 0 · Q129 · MCQ
Consider a two particle system with particles having masses $m_{1}$ and $m_{2}$ . If the first particle is pushed towards the center of mass through a distance $d,$ by what distance should the second particle is moved, so as to keep the…2006 · Shift 0 · Q130 · MCQ
The block of mass $M$ moving on the frictionless horizontal surface collides with the spring of spring constant $k$ and compresses it by length $L .$ The maximum momentum of the block after collision is Includes diagram2005 · Shift 0 · Q147 · MCQ
A mass $^{'} m^{'}$ moves with a velocity $^{'} v^{'}$ and collides inelastically with another identical mass. After collision the $1^{s t}$ mass moves with velocity $\frac{v}{3}$ in a direction perpendicular to the initial direction of… Includes diagram2005 · Shift 0 · Q148 · MCQ
A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $^{'} F^{'}$ is applied at the point $P$ parallel to $A B,$ such that the object has only the translational motion without… Includes diagram2005 · Shift 0 · Q151 · MCQ
A body $A$ of mass $M$ while falling vertically downloads under gravity breaks into two-parts; a body $B$ of mass $\frac{1}{3} M$ and a body $C$ of mass $\frac{2}{3} M .$ The center of mass of bodies $B$ and $C$ taken together shifts compared…2005 · Shift 0 · Q182 · MCQ
A machine gun fires a bullet of mass $40 g$ with a velocity $1200 m s^{- 1} .$ The man holding it can exert a maximum force of $144 N$ on the gun. How many bullets can he fire per second at the most?2004 · Shift 0 · Q162 · MCQ
Consider the following two statements : $A .$ Linear momentum of a system of particles is zero $B .$ Kinetic energy of a system of particles is zero. then2003 · Shift 0 · Q180 · MCQ
Two identical particles move towards each other with velocity $2 v$ and $v$ respectively. The velocity of center of mass is2002 · Shift 0 · Q179 · MCQ