Block `A` of mass `m` is placed on a plank `B`. A light support `S` is fixed on plank `B` and is attached with the block A with a spring of spring constant `K`. Consider that initially spring is in its natural length. If the plank `B` is given an acceleration a, then maximum compression in the spring is `(xma)/(k)`. Find the value of `x` (All the surface are smooth)

Options

A. `(ma)/(2K)`
B. `(2ma)/(K)`
C. `(ma)/(K)`
D. `(2ma)/(K)`

Answer

B

Explanation

Block `A` of …………..

In the frame of `B`
`W_("pseduo")+W_("spring") = Delta K = 0`
`+ ma x_(max) + (- (1)/(2)Kx_(max)^(2))=0`
`x_(max) = (2ma)/(K)`