Question

Initially wedges was at rest and spring is in natural length. Now a solid sphere of same mass that of wedge is attached to the spring and is released as shown in figure. (assume sphere is in pure Rolling). The maximum extension in spring is:

• A. $\frac{2}{5}meter$
• B. $\frac{3}{5}meter$
• C. $\frac{4}{6}meter$
• D. $2meter$

Answer 1

The correct option is A $\frac{2}{5}meter$

At max. extension linear momentum of systam is zero and both ball and wedge will be at rest,
Equating the gravitational potential energy to the elastic potential energy we get

$mg\times x\times \frac{3}{5}=\frac{1}{2}\left(3mg\right)\cdot x^2$ (here $xsin\theta =x\times \frac{3}{5}$ is the component of displacement in the vertical direction)

$x=\frac{2}{5}m$