A system of wedge and block as shown in figure, is released with the spring in its natural length. All surfaces are frictionless. Maximum elongation in the spring will be
.

Options

A. `(2 mg sin theta)/K`
B. `(mg sin theta)/K`
C. `(4mg sin theta)/K`
D. `(mg sin theta)/(2K)`

Answer

A

Explanation

Decrease in gravitational potential energy of block
= increase in spring potential energy
`:. mg (x_(m)sin theta) =1/2 Kx_(m)^(2)`
`:. X_(m) =(2 mg sin theta)/K`