Question

Assertion :If the velocity of centre of mass of a system is zero then the kinetic energy of the system may be greater than zero. and Reason: Kinetic energy of the system is given by $\frac{1}{2}\int v^{2}dm$

• 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

We know,

$v_{cm}=\int vdm$

$KE=\int v^{2}dm$

V in the formula of velocity of centre of mass is velocity (vector),

Which can result to zero,

But v in formula for Kinetic energy of the system is speed of the

particles,

and also $v^2$ is always positive which can never sum up to

zero( Only if v not equal to 0).

Hence the assertion is correct and the reason is the correct explanation of the

Assertion.

Hence option $\text{A}$ is correct answer.