Question

A block of mass m is released at rest from a point P of a rough circular path of radius r as shown in the figure. There is a spring of stiffness k at the other end of the path. (acceleration due to gravity = g)
The maximum spring deflection is

• A. $\text{independent of}r$
• B. $\text{more than}\sqrt{2mgr/k}$
• C. $\text{equal to}\sqrt{2mgr/k}$
• D. $\text{less than}\sqrt{2mgr/k}$

Answer 1

The correct option is D $\text{less than}\sqrt{2mgr/k}$

$\text{Change in kinetic energy = Net work done}$

$0-\frac{1}{2}\times m\times v^2=\frac{-1}{2}k{x}^2[\because v=\sqrt{2gr}]$

$\therefore m\times 2gr=k{x}^2$

$\therefore x=\sqrt{\frac{2mgr}{k}}$

Here, in this answer we assume that it is a smooth surface. So friction force is neglected.

Consider the surface to be rough, so deflection

$\delta <x$.

$\therefore \delta <\sqrt{\frac{2mgr}{k}}$