System of Particles and Rotational Motion - Result Question 83
90. A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest ) on the inclined plane, then
[1993]
(a) solid sphere reaches the bottom first
(b) solid sphere reaches the bottom last (c) disc will reach the bottom first
(d) all reach the bottom at the same time
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Answer:
Correct Answer: 90. (a)
Solution:
- (a) For solid sphere, $\frac{K^{2}}{R^{2}}=\frac{2}{5}$
For disc and solid cylinder, $\frac{K^{2}}{R^{2}}=\frac{1}{2}$
As $\frac{K^{2}}{R^{2}}$ for solid sphere is smallest, it takes minimum time to reach the bottom of the incline
When bodies of different shapes are allowed to roll down an incline, then velocity at the bottom of incline, acceleration and time taken in reaching the bottom depends on $\frac{K^{2}}{R^{2}}$. If the body has less moment of inertia then $\frac{K^{2}}{R^{2}}$ will be less, then it will take less time in reaching the bottom.
