Question 244 of 280
A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is where _____
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Answer: 4
Applying Mechanical Energy conservation :
$\begin{aligned}
& \Rightarrow 0+\mathrm{Mgh}=\frac{1}{2} \mathrm{mv}^2\left(1+\frac{\mathrm{k}^2}{\mathrm{R}^2}\right)+0 \\
& \Rightarrow \mathrm{~V}=\sqrt{\frac{2 \mathrm{gh}}{1+\frac{\mathrm{k}^2}{\mathrm{R}^2}}}
\end{aligned}$
So Ratio of velocities
Rounding off
$\begin{aligned}
& \Rightarrow 0+\mathrm{Mgh}=\frac{1}{2} \mathrm{mv}^2\left(1+\frac{\mathrm{k}^2}{\mathrm{R}^2}\right)+0 \\
& \Rightarrow \mathrm{~V}=\sqrt{\frac{2 \mathrm{gh}}{1+\frac{\mathrm{k}^2}{\mathrm{R}^2}}}
\end{aligned}$
So Ratio of velocities
Rounding off