Question

Which of the following statements is true?
A. When two hoops with different radii roll down an inclined plane without slipping, they reach the bottom at the same time.
B. If a body is rotating about an axis without any external torques, and its size doubles, it will speed up to double the angular velocity.
C. Two disks roll down an inclined plane without slipping. The one with a smaller radius will always reach the bottom first independent of their masses.
D. When two objects roll down an inclined plane without slipping, they have the same velocity when they reach the bottom only if they have the same mass.
E. The moment of inertia of an object would be different on the surface of the moon than it is on the surface of the Earth

Answer 1

Solution

(A) When two hoops with different radii roll down an inclined plane without slipping, they reach the bottom at the same time.

Is the correct answer for this question.

Because

Acceleration of an body moving on inclined plane without sleeping then it's linear acceleration can be given as

$a=\frac{gsin\theta}{1+\frac{I}{mr^2}}$

Ratio of $\frac{I}{mr^2}$ Will be equal for both disk

So acceleration will be equal .

If acceleration is equal then both hoop take same time to reach at bottom point of inclined plane.