Solve the following :


Figure (8-E15) shows a smooth track, a part of which is a circle of radius $\mathrm{R}$. A block of mass $n$ pushed against a spring of spring constant $k$ fixed at the left end and is then released. Find the in compression of the spring so that the block presses the track with a force mg when it reaches the point $\mathrm{P}$, where the radius of the track is horizontal.


According to figure,

$\left(m v^{2}\right) / R=m g$

$\mathrm{v}=\sqrt{g R}$

Energy is same at $A$ and $P$

$\frac{\mathrm{mgR}+2 \mathrm{mgR}}{2}$

$\mathrm{X}=\sqrt{\frac{3 m g R}{K}}$


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