Question

A ring takes time $t_1$ in slipping down an inclined plane of length L, whereas it takes time $t_2$ in rolling down the same plane. The ratio of $t_1$ and $t_2$ is :

• A. $2^{\frac{1}{2}}:1$
• B. $1:2^{\frac{1}{2}}$
• C. $1:2$
• D. $1:2^{\frac{1}{4}}$

Answer 1

The correct option is B $1:2^{\frac{1}{2}}$

while slipping

$acc=g\sin \theta$

$t_1=\sqrt{\frac{2l}{g\sin \theta }}$

$acc=\frac{g\sin \theta }{2}$

$t_2=\sqrt{\frac{2l}{g\sin \theta }\times 2}$

$\Rightarrow \frac{t_1}{t_2}=\frac{1}{2^{\frac{1}{2}}}=1:2^{\frac{1}{2}}$

Hence,

option $\left(B\right)$ is correct answer.