Question

First time a ring slips without rolling on an inclined plane and second time it rolls down without slipping. The ratio of accelerations produced in both situations will be:

(a) 1:1

(b) 2:1

(c) 1:2

(d) 4:1

Answer 1

Correct option is : (b) 2:1

Ratio of accelerations in given situations:

\(\frac{a_1}{a_2} = \frac{\frac{g\sin\theta}{g\sin\theta}}{1 + \frac{K^2}{R^2}} = 1 + \frac{K^2}{R^2}\) 

For ring I = MK² =  MR² \(\Rightarrow\frac{K^2}{R^2} = 1\) 

\(\therefore\ \frac{a_1}{a_2} = 1 + 1 = 2\)

\(\therefore\ a_1 : a_2 = 2:1\) 

Thus option (b) is correct.