Question

The ratio of the accelerations for a solid sphere (mass 'm' and radius 'R') rolling down an incline of angle ${}^{\prime }{\theta }^{\prime }$ without slipping and slipping down the incline without rolling is:

• A. 7 : 5
• B. 5 : 7
• C. 2 : 3
• D. 2 : 5

Answer 1

The correct option is B 5 : 7

Case - (I)
We know that,
a = g sin $\theta$

Case - (II)
$a^{\prime }=\frac{gsin\theta }{1+\frac{K^2}{R^2}}(here\frac{K^2}{R^2}=\frac{2}{5})$

$\therefore \frac{a^{\prime }}{a}=(1+\frac{K^2}{R^2})gsin\theta$
$=\frac{1}{1+\frac{2}{5}}=\frac{1}{\frac{7}{5}}=\frac{5}{7}$