New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Work Power and Energy question

2024 · 29 Jan · Shift 1 · Q79

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Work Power and Energy
2024 · 29 Jan · Shift 1 · Q79

Work Power and Energy question

2024 · 29 Jan · Shift 1 · Q79

JEE MainPhysicsWork Power and EnergyMCQ+4 / −1

The potential energy function (in

J

) of a particle in a region of space is given as

U=\left(2 x^2+3 y^3+2 z\right)

. Here

x, y

and

z

are in meter. The magnitude of

x

-component of force (in

N

) acting on the particle at point

P(1,2,3) \mathrm{m}

is :

A
4
B
2
C
8
D
6

View written solutionFree

Correct answer: A

The force is related to potential energy by $\vec F=-\nabla U$ So the $x$ -component of force is $F_x=-\frac{\partial U}{\partial x}$
Given $U=2x^2+3y^3+2z$ Differentiate with respect to $x$ : $\frac{\partial U}{\partial x}=4x$ Hence, $F_x=-4x$
At point $P(1,2,3)$ , we have $x=1$ . Therefore, $F_x=-4(1)=-4\,\text{N}$
The question asks for the magnitude of the $x$ -component: $|F_x|=4\,\text{N}$
Therefore, the correct option is: $\boxed{\text{A: }4}$

More from Work Power and Energy

A bob of mass ' $m$ ' is suspended by a light string of length ' $L$ '. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position B. The ratio of kinetic… Includes diagram2024 · MCQ
A particle is placed at the point $A$ of a frictionless track $A B C$ as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is : (Take $g = 10 m / s^{2}$ ). Includes diagram2024 · MCQ
A block of mass $6 0^{\circ}$ is pushed up a surface inclined to horizontal at an angle of $6 0^{\circ}$ by a force of $10 m$ parallel to the inclined surface as shown in figure. When the block is pushed up by $10 m$ … Includes diagram2024 · MCQ
A body of mass $F = (6 t \hat{i} + 6 t^{2} \hat{j}) N$ begins to move under the action of a time dependent force given by $F = (6 t \hat{i} + 6 t^{2} \hat{j}) N$ . The power developed by the force at the time $t$ is given by:2024 · MCQ
A small particle moves to position $5 \hat{i} - 2 \hat{j} + \hat{k}$ from its initial position $2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ under the action of force $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N$ . The value of work done will be …2023 · Numerical
A block is fastened to a horizontal spring. The block is pulled to a distance $x = 10 cm$ from its equilibrium position (at $x = 0$ ) on a frictionless surface from rest. The energy of the block at $x = 5 cm$ is $0.25 J$ …2023 · Numerical
A force $F = (5 + 3 y^{2})$ acts on a particle in the $y$ -direction, where $F$ is in newton and $y$ is in meter. The work done by the force during a displacement from $y = 2 m$ to $y = 5 m$ is …2023 · Numerical
A particle of mass $2 x$ moves in a straight line with retardation $2 x$ , where $x$ is the displacement in SI units. Its loss of kinetic energy for above displacement is $(\frac{10}{x})^{- n}$ J. The value of $n$ …2023 · Numerical