Question

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

• A. $\frac{2mg\sin \theta }{K}$
• B. $\frac{mg\sin \theta }{K}$
• C. $\frac{4mg\sin \theta }{K}$
• D. $\frac{mg\sin \theta }{2K}$

Answer 1

The correct option is A $\frac{2mg\sin \theta }{K}$

By applying law of conservation of energy on whole system

if mass slides down then its potential energy decreases

mass slides x on inclined plane then its height decreased by cos component of x

then potential energy decreases of mass is

$PE=mgxcos\theta$

this energy is gained by spring as kinetic energy

$PE=mgxcos\theta =\frac{1}{2}k{x}^2$

from this we get,

$x=\frac{2mgcos\theta }{k}$