Question

Assertion :In the system shown in figure spring is first stretched the left to oscillate. At some instant kinetic energy of mass is $K$. At the same instant kinetic energy of mass 2m should be $\frac{K}{2}$. Reason: Their linear momenta are equal and opposite and $K=\frac{p^2}{2m}$ or $K\propto \frac{1}{m}$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Since the total linear momentum of the system is zero initially. Thus according to conservation of linear momentum, final linear momentum of the system must also be zero. So, both masses move with equal magnitude to linear momentum but in opposite direction i.e. $|p_1|=|p_2|$

Kinetic energy of mass $m$, $K=\frac{|p_1{|}^2}{2m}$

Kinetic energy of mass $2m$, $K^{\prime }=\frac{|p_2{|}^2}{2\left(2m\right)}$

But $|p_1|=|p_2|$

$⟹$ $K^{\prime }=\frac{K}{2}$

Hence option A is correct.