First slide

The steps in collision

Question

A block A of mass M moving with speed u collides elastically with block B of mass m which is connected to block C of mass m with a spring.
When the compression in spring is maximum, the velocity of block C with respect to block A is
(Neglect the friction everywhere)

Moderate

A

zero
B

$(\frac{M}{M + m}) u$
C

$(\frac{m}{M + m}) u$
D

$(\frac{m}{M}) u$

Solution

Here, $v_{A} = (\frac{M - m}{M + m}) u$ and $v_{B} = \frac{2 M u}{M + m}$
Velocity of C at maximum compression, v_c = v_B/2
$∴ v_{C} = \frac{1}{2} [\frac{2 M}{M + m}] u = (\frac{M}{M + m}) u$
$∴ v_{C A} = v_{C} - v_{A} = (\frac{m}{M + m}) u$

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