Question

A cylinder rolls up an inclined plane at an angle of 30°. At the bottom of the inclined plane, the centre of mass of the cylinder has speed of 5 m/s. How long will it take to return to the bottom?

• A. 2 s
• B. 3 s
• C. 1.5 s
• D. 4 s

Hint:

In problems involving rolling motion, use conservation of mechanical energy. The time taken to return to the bottom is the same as the time taken to reach the top, doubled.

Answer 1

The Correct Option is B

When a cylinder rolls up an inclined plane, its motion is a combination of translational and rotational motion. The total mechanical energy is conserved. The speed of the cylinder at the bottom of the incline is given as 5 m/s. We can use the principle of conservation of energy to find the time it will take to return to the bottom.

Since the energy is conserved, the time to reach the maximum height is the same as the time to return to the bottom, and thus the total time is twice the time taken to reach the maximum height. From the calculations, the time is found to be 3 seconds.

Hence, the correct answer is (b).