First slide

Rolling motion

Question

The ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’) rolling down and incline of angle 'θ' without slipping and slipping down the incline without rolling is

Moderate

A

2:3
B

2:5
C

7:5
D

5:7

Solution

For a round object rolling without slipping down an incliend surface, aaceleration is given by $\large {a_1} = \frac{{g\sin \theta }}{{(1 + {I_c}/m{R^2})}}$
and for the same object slipping down for a solid sphere a₂ = g(sinθ)
For a solid sphere $\frac {a_1}{a_2}=\frac {1}{1+\frac {\frac 25mR^2}{mR^2}$ $\frac {a_1}{a_2}=\frac {1}{1+\frac {\frac 25mR^2}{mR^2}$ = 5/7

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