One end of an spring is connected with a smooth block with the other end with rear wall of a truck as shown in figure. initially, the system is at rest if track start to its accelerate with a constant acceleration then the block (relative to track)

Options

A. will remain stationary.
B. will start oscillation with constant amplitude.
C. will start stationary with increasing amplitude.
D. moves such that length of the spring first increases and then becomes constant.

Answer

B

Explanation

In released frame fixed to the acceleration truck , we may consider the block as shown in figure A psende force `F = ma` is acting on the block toeard left since magnitude of the force is consider , therefore maximum elongation of the spring will be equal to `(2ma)/(k)`

But the equilibrium elogation of this spring should be equal to `(ma)/(K)` it mean block will start to perform oscillation and the amplitude of oscillation will equal to `(2ma)/(K) - (ma)/(K) = (ma)/(K)`