Question

The maximum potential energy that the spring connecting blocks A and B can have as a consequence of collision of block C with A is (ignore any friction). Assume the collision between C and A to be elastic.

• A. $m{v}_0^2$
• B. $\frac{m{v}_0^2}{2}$
• C. $\frac{m{v}_0^2}{4}$
• D. $\frac{2m{v}_0^2}{3}$

Answer 1

The correct option is C

$\frac{m{v}_0^2}{4}$

‘C’ comes to rest immediately after collision. A starts moving with $v_0$. At the instant of maximum compression or elongation, relative velocity of A with respect to B would be zero and hence A and B would be moving with a common velocity. From conservation of momentum, $m{v}_0=2mv\Rightarrow v=\frac{v_0}{2}$.

Hence, from conservation of energy: $(P.E{)}_{\text{max}}=\frac{1}{2}m{v}_0^2-\frac{1}{2}(2m){\left(\frac{v_0}{2}\right)}^2=\frac{1}{2}m{v}_0^2-\frac{1}{4}m{v}_0^2=\frac{1}{4}m{v}_0^2$