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If a body looses half of its velocity on...

If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?

A

`1 cm`

B

`2 cm`

C

`3 cm`

D

`4 cm`

Text Solution

Verified by Experts

The correct Answer is:
A
Let initial velocity of body at point `A` is `v, AB` is `3cm`.

From `v^(2) = u6(2) - 2as`
`((v)/(2))^(2) = v^(2) - 2a xx 3`
`a = v^(2)/(8)`
Let on penetrating `3cm` in a wooden block, the body moves `x` distance from `B` to `C`.
So, for `B` to `C`
`u = (v)/(2), v = 0`,
`x = x, a = (v^(2))/(8)` (deceleration)
`:. (0)^(2) = ((v)/(2))^(2) - 2. (v^(2))/(8).x`
`x = 1`
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