JEE Main 2021 · Physics · Work, Energy and Power · hard

A block of mass 2 kg moving at 6 m s^-1 on a smooth horizontal surface strikes a light spring (k=300 N m^-1) attached to a stationary 4 kg block. The…

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A block of mass

2\ \mathrm{kg}

moving at

6\ \mathrm{m\,s^{-1}}

on a smooth horizontal surface strikes a light spring (

k=300\ \mathrm{N\,m^{-1}}

) attached to a stationary

4\ \mathrm{kg}

block. The maximum compression of the spring is

A. $0.2\ \mathrm{m}$
B. $0.8\ \mathrm{m}$
C. $0.69\ \mathrm{m}$
D. $0.4\ \mathrm{m}$

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Answer: (D) $0.4\ \mathrm{m}$

At maximum compression both blocks share the same velocity (that of the centre of mass), so the kinetic energy lost in the centre-of-mass frame is stored in the spring:

\tfrac12\mu v_{rel}^2=\tfrac12 kx^2

with

\mu=\dfrac{2\times4}{6}=\dfrac43\ \mathrm{kg}

. Thus

\tfrac12\cdot\tfrac43\cdot36=24\ \mathrm{J}=150x^2\Rightarrow x=0.4\ \mathrm{m}

. Using the full

\tfrac12(2)(36)=36\ \mathrm{J}

would wrongly give

0.69\ \mathrm{m}

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