Question

Assertion :The kinetic energy of system appears minimum relative to an observer moving with a velocity of $3\hat{i}m/s$. Reason: The kinetic energy of any $2$ block system is $\frac{1}{2}M{V}_v^2+\frac{1}{2}\mu V_{rel}^2$ where symbols have their usual meanings.

• 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 and Reason is correct

Answer 1

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

For the observer moving with velocity $3\hat{i}m/s$ the relative velocity with respect to him will be minimum

$V_{1,0}=(1-3)\hat{i}=-2\hat{i}m/s$

Similarly,

$V_{2,0}=(9-3)\hat{i}=1\hat{i}m/s$

Kinetic energy of system containing a moving observer of mass M with velocity V will be

$K.E=\frac{1}{2}m{v}^2+\frac{1}{2}\mu (V_{rel}{)}^2$