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Standard XII

Physics

Examples

A small ball ...

Question

A small ball is projected horizontally between two large blocks. The ball is given a velocity $V$ m/s and each of the large blocks move uniformly with a velocity of $2 V$ m/s. The ball collides elastically with the blocks. If the velocity of the blocks do not change due to the collision, then find out the velocity of the ball after the $2^{n d}$ collision.

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Solution

The correct option is C
9V

Use the following result:

$e$ = $\frac{v_{2} - v_{1}}{u_{1} - u_{2}}$

$\Rightarrow$ 1 = $\frac{- v_{0} (- v_{1})}{u_{1} - (- v_{0})} \Rightarrow v_{1} = u_{1} + 2 v_{0}$

Using the above result:

Now velocity after first collision

$V^{'}$ = $V + 2 (2 V)$ = $5 V$

Velocity after second collision

$V^{''}$ = $V^{'} + 2 (2 V)$ = $5 V + 4 V$ = $9 V$

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The correct option is C 9V Use the following result: e = v2−v1u1−u2 ⇒ 1 = −v0(−v1)u1−(−v0) ⇒ v1 = u1 + 2v0 Using the above result: Now velocity after first collision V′ = V+2(2V) = 5V Velocity after second collision V′′ = V′+2(2V) = 5V+4V = 9V