Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
        A cannonball and a marble roll from rest down an incline. Which gets to the bottom first?
5 years ago

396 Points
							Both, the cannonball and the marble rolls from rest down the incline plane in the same time. It is obvious that the radius of the marble will be smaller than the radius of the cannonball, therefore the marble will have smaller rotational inertia than the cannonball and will make more revolutions per second.The distance travelled by the cannonball in one revolution is much greater than the distance travelled by the marble. Therefore the motion of the balls is such that the larger distance travelled by the cannonball in each revolution is compensated by the large number of revolutions made by the marble in the same time.Therefore the cannonball and the marble reach the bottom in the same time.

5 years ago
S S Mathur
19 Points
							In the case of any ball rolling down an inclined place without slipping: the potential energy mgh at the top of the incline is equal to the KE at the bottom. The KE = translational KE ($\frac{1}{2}mv^{2}$) + rotational KE ($\frac{1}{2}I\omega ^{2}$).  For a sphere, $I=\frac{2}{5}mr^{2}$ and $\omega =\frac{v}{r}$. Therefore at the bottom of the incline velocity $v=\sqrt{\frac{10}{7}gh}$. Since $v^{2}=2as$ (s being the length of the inclined plane), and $\frac{h}{s}=sin\theta$ (the angle of the incline), acceleration $a=\frac{5gsin\theta }{7}$. Both velocity at the bottom and acceleration are independent of the mass or radius of the ball, and depend only on the length of the inclined plane and its angle. Therefore the time taken by both of them to reach the bottom is the same.

3 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Mechanics

View all Questions »

### Course Features

• 101 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution

### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions