Question

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

A. (a) `sqrt(m/k)`
B. (b) `alphasqrt(m/k)`
C. (c) `alphasqrt((m)/(2k))`
D. (d) `2alphasqrt(m/k)`

Answer 1

Correct Answer - B
Solving this question relative to the frame (car) of reference. For maximum velocity (relative to frame), the block must be in equilibrium position.
Let `x_0` be the equilibrium elongation in spring, then
`ma=kx_0`
From work-energy theorem,
`(mv^2)/(2)-0=-(kx_0^2)/(2)+ma x_0`
Solving the above equation, we get `v=asqrt(m/l)`
This question is an application of using the work-energy theorem in non-inertial frame of reference.