System of Particles and Rotational Motion - Result Question 75
82. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first? (a) Disk
(b) Sphere
[2016]
(c) Both reach at the same time
(d) Depends on their masses
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Answer:
Correct Answer: 82. (b)
Solution:
- (b) Time of descent $\propto \frac{K^{2}}{R^{2}}$
Order of value of $\frac{K^{2}}{R^{2}}$
for disc; $\frac{K^{2}}{R^{2}}=\frac{1}{2}=0.5$
for sphere; $\frac{K^{2}}{R^{2}}=\frac{2}{5}=0.4$
(sphere) $<$ (disc)
$\therefore \quad$ Sphere reaches first
The value $\frac{K^{2}}{R^{2}}$ is a measure of moment of inertia. Its. value is fixed for a particular shape of the body and independent of mass and readius of the body.
