Question

Assertion :A constant force $F$ is applied on two blocks and one spring system as shown in figure. Velocity of centre of mass increases linearly with time. Reason: Acceleration of centre of mass is constant.

• 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

$a_{cm}=b$; where $b$ is a constant.
$a_{cm}=\frac{d{v}_{cm}}{dt}\Rightarrow \int d{v}_{cm}=\int bdt\Rightarrow v_{cm}=bt+c$; where $c$ is the integration constant
At t=0, $v_{cm}=0\Rightarrow c=0$;
$\Rightarrow v_{cm}=bt$;
Both Assertion and Reason are correct.