Home
Class 11
PHYSICS
A ball falls under gravity from a height...

A ball falls under gravity from a height 10 m with an initial velocity `v_0`. It hits the ground, loses 50% of its energy in collision and it rises to the same height, what is the value of `v_0`? 

A

14 m/s

B

7 m/s

C

28 m/s

D

9.8 m/s

Text Solution

Verified by Experts

The correct Answer is:
A

Let v be the velocity of the ball when it hits the ground.
then `v^2 = v_0^2 + 2gh = v_0^2 + 2 xx 9.8 xx 10`
or `v^2 = v_0^2 + 196`
Let `v.` be the velocity after impect and it rise same height 10 m.
`:. V.^(2) - 0 = 2 xx 9.8 xx 10 = 196 or v. = 14 m//s`
Ratio of kinetic energy before impact and after impact
`(1/2 mv^2)/(1/2 mv.^2) = (v^2)/(v.^2) = (v_0^2 + 196)/(196) = 2 " or " v_0 = 14 m//s` .
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • WORK, ENERGY AND POWER

    MTG GUIDE|Exercise NEET CAFE (TOPICWISE PRACTICE QUESTIONS) (MOTIN IN A VERTICAL CIRCLE)|7 Videos
  • WORK, ENERGY AND POWER

    MTG GUIDE|Exercise NEET CAFE (TOPICWISE PRACTICE QUESTIONS) (COLLISIONS)|35 Videos
  • WORK, ENERGY AND POWER

    MTG GUIDE|Exercise NEET CAFE (TOPICWISE PRACTICE QUESTIONS) (POTENTIAL ENERGY AND CONSERVATIVE FORCES)|19 Videos
  • THERMODYNAMICS

    MTG GUIDE|Exercise AIPMT/NEET (MCQs)|26 Videos

Similar Questions

Explore conceptually related problems

A ball falls undal gravity from a height of 10m with an initial downward velocity u. It collides with ground, loses halft its energy and then rises back to the same height. Find the initial velocity u.

A ball falls under gravity from a hight of 10 m height of 10 m wioth an initial downward velocity u .If collides with the gound , loses 50% of its energy in collision and then rises back back to the same heighrt .Find the initial velocity u.

Knowledge Check

  • A ball falls under gravity from a height of 10 m with an initial downward velocity u. It collides with the ground, losses 50% of its energy in collision and then rises back to the same height. The initial velocity u is

    A
    `7 m s^(-1)`
    B
    `25 m s^(-1)`
    C
    `14 m s^(-1)`
    D
    `28 m s^(-1)`
  • A ball is thrown vertically downwards from a height of 20m with an intial velocity v_(0) . It collides with the ground, loses 50% of its energy in collision and rebounds to the same height. The intial velocity v_(0) is (Take, g =10 ms^(-2) )

    A
    `14ms^(-1)`
    B
    `20ms^(-1)`
    C
    `28ms^(-1)`
    D
    `10ms^(-1)`
  • A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_0 . It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v_0 is (take g = 10 ms^(-2))

    A
    `28 ms^(-1)`
    B
    `10 ms^(-1)`
    C
    `14 ms^(-1)`
    D
    `20 ms^(-1)`
  • Similar Questions

    Explore conceptually related problems

    A body is allowed to fall freely under gravity from a height of 10m. If it looses 25% of its energy due to impact with the ground, then the maximum height it rises after one impact is

    A ball is thrown vertically down from height of 40 m from the ground with an initial velocity 'v'. The ball hits the ground, loses (1)/(3)rt of its total mechanical energy and rebounds back to the same height. If the acceleration due to gravity is 10 "ms"^(-2) , the value of 'v' is

    A ball is falling freely from a certain height. When it reached 10 m height from the ground its velocity is v_(0) . It collides with the horizontal ground and loses 50 % of its energy and rises back to height of 10 m . The value of velocity v_(0) is

    A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50% of its energy and rebounds to the same height. The initial velocity of its projection is

    A body is allowed to fall freely under gravity from a height of 10 m. If it loses 25% of its energy on impact with the ground, to what height will it rise after one impact?