Question

A block of mass m is connected to a spring of spring constant K as shown in figure. The frame in which block is placed is given an acceleration 'a' towards left. Neglect friction between block and frame walls. The maximum velocity of the block relative to frame is

• A. $\sqrt{\frac{m}{k}}$
• B. $a\sqrt{\frac{m}{k}}$
• C. $a\sqrt{\frac{m}{2k}}$
• D. $2a\sqrt{\frac{m}{k}}$

Answer 1

The correct option is B $a\sqrt{\frac{m}{k}}$

Solve this question relative to (car) frame of reference. For maximum velocity (relative to frame) the block must be in equilibrium position.
Let $x_0$ is the elongation in spring in equilibrium then, $ma={kx}_0$
From work energy theorem.
$\frac{m{v}^2}{2}-0=\frac{k{x}_0^2}{2}+ma\times x_0$
Solving the above equation we get $v=a\sqrt{\frac{m}{k}}$