Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Motion in A Straight Line question

2023 · 12 Apr · Shift 1 · Q56
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.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Motion in A Straight Line
  5. /2023 · 12 Apr · Shift 1 · Q56

Motion in A Straight Line question

2023 · 12 Apr · Shift 1 · Q56

JEE MainPhysicsMotion in A Straight LineMCQ+4 / −1
A ball is thrown vertically upward with an initial velocity of 150 m/s150 \mathrm{~m} / \mathrm{s}150 m/s. The ratio of velocity after 3 s3 \mathrm{~s}3 s and 5 s5 \mathrm{~s}5 s is x+1x\frac{x+1}{x}xx+1​. The value of xxx is ‾\underline{\hspace{2cm}}​. {\left\{\right.{ take, g=10 m/s2}\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right\}g=10 m/s2}
  1. A
    −5-5−5
  2. B
    10
  3. C
    5
  4. D
    6
View written solutionFree

Correct answer: C

  1. Use the equation for velocity under gravity

For a ball thrown vertically upward with initial velocity u=150 m/su=150\,\text{m/s}u=150m/s, its velocity after time ttt is

v=u−gtv = u - gtv=u−gt

with g=10 m/s2g=10\,\text{m/s}^2g=10m/s2.

  1. Velocity after 333 s

v3=150−10(3)=150−30=120 m/sv_3 = 150 - 10(3) = 150 - 30 = 120\,\text{m/s}v3​=150−10(3)=150−30=120m/s

  1. Velocity after 555 s

v5=150−10(5)=150−50=100 m/sv_5 = 150 - 10(5) = 150 - 50 = 100\,\text{m/s}v5​=150−10(5)=150−50=100m/s

  1. Form the ratio

Given that the ratio of velocity after 333 s and 555 s is

v3v5=x+1x\frac{v_3}{v_5} = \frac{x+1}{x}v5​v3​​=xx+1​

Substitute the values:

120100=x+1x\frac{120}{100} = \frac{x+1}{x}100120​=xx+1​

65=x+1x\frac{6}{5} = \frac{x+1}{x}56​=xx+1​

  1. Solve for xxx

Cross-multiply:

6x=5(x+1)6x = 5(x+1)6x=5(x+1)

6x=5x+56x = 5x + 56x=5x+5

x=5x = 5x=5

  1. Check options
  • A: −5-5−5 ✗
  • B: 101010 ✗
  • C: 555 ✓
  • D: 666 ✗

Hence, the correct option is C.

PreviousNext

More from Motion in A Straight Line

  • Two trains 'A' and 'B' of length 'l' and '4l' are travelling into a tunnel of length 'L' in parallel tracks from opposite directions with velocities 108 km/h and 72 km/h,…2023 · MCQ
  • The distance travelled by an object in time t is given by s=(2.5)t2. The instantaneous speed of the object at t=5 s will be:2023 · MCQ
  • A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then…2023 · MCQ
  • The position of a particle related to time is given by x=(5t2−4t+5)m. The magnitude of velocity of the particle at t=2s will be :2023 · MCQ
  • The velocity time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in time 0 to 10s is : Includes diagram2023 · MCQ
  • A car travels a distance of 'x' with speed v1​ and then same distance 'x' with speed v2​ in the same direction. The average speed of the car is :2023 · MCQ
  • The distance travelled by a particle is related to time t as x=4t2. The velocity of the particle at t=5s is :-2023 · MCQ
  • A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ​ ms −2. (Given g = 10…2023 · Numerical