First slide

Potential energy

Question

Two identical blocks A and B, each of mass ‘m’ resting on smooth floor are connected by a light spring of natural length L and the spring constant K, with the spring at its natural length. A third identical block C (mass m) moving with a speed v along the line joining A and B collides with A. The maximum compression in the spring is………….

Difficult

A

$v \sqrt{m / 2 k}$
B

$m \sqrt{\frac{v}{2 k}}$
C

$\sqrt{\frac{m v}{2 k}}$
D

$\frac{m v}{2 k}$

Solution

$A t t h e t i m e o f m a x i m u m c o m p r e s s i o n b o t h w i l l m o v e w i t h t h e s a m e v e l o c i t y s a y v_{1} f r o m c o n s e r v a t i o n o f l i n e a r m o m e n t u m m v = 2 m v_{1} v_{1} = \frac{v}{2} a n d f r o m c o n s e r v a t i o n o f e n e r g y \frac{1}{2} m v^{2} = \frac{1}{2} m {(\frac{v}{2})}^{2} \times 2 + \frac{1}{2} k x^{2} s o l v i n g x = v \sqrt{\frac{m}{2 k}}$

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