Question

A bead of mass $m$ can slide without friction on a fixed circular horizontal ring of radius $3R$ having a centre at the point $C$ . The bead is attached to one of the ends of spring with spring constant $k$ . The natural length of spring is $R$ and the other end of the spring is fixed at point $O$ as shown in the figure. If the bead is released from position $A$ , then the kinetic energy of the bead when it reaches point $B$ is

• A. $\frac{25}{2}k{R}^2$
• B. $\frac{9}{2}k{R}^2$
• C. $8k{R}^2$
• D. $12k{R}^2$

Answer 1

Answer: (C)

Given,
Mass of bead $=m$
The radius of circular horizontal ring $=3R$
The natural length of spring $=R$
According to the conservation of energy,
$K{E}_i+P{E}_i=K{E}_f+P{E}_f$
$\Rightarrow 0+\frac{1}{2}k{\left[OA-R\right]}^2=K{E}_f+\frac{1}{2}k{\left[OB-R\right]}^2$
$\Rightarrow 0+\frac{1}{2}k{\left[5R-R\right]}^2=K{E}_f+\frac{1}{2}k{\left[R-R\right]}^2$
$\Rightarrow K{E}_f=8k{R}^2$