Question

A solid sphere of mass 1 kg and radius 25 cm is at rest at the top of an inclined plane of height 175 cm and angle of inclination 30°. If the sphere rolls down without slipping, the maximum velocity of the sphere when it reaches the bottom of the inclined plane is (Acceleration due to gravity = 10 m/s²)

• A. 5 m/s
• B. 10 m/s
• C. 7 m/s
• D. 14 m/s

Hint:

For rolling motion, remember that the kinetic energy consists of both translational and rotational components.

Answer 1

The Correct Option is A

Using energy conservation, the potential energy lost by the sphere is converted into kinetic energy. The total kinetic energy at the bottom is the sum of the translational and rotational kinetic energy: \[ mgh = \frac{7}{10} m v^2 \] where \( h = 175 \, \text{cm} = 1.75 \, \text{m} \).
Using \( g = 10 \, \text{m/s}^2 \), we find: \[ 1.75 \times 10 = \frac{7}{10} v^2 \Rightarrow v = 5 \, \text{m/s} \]
Thus, the maximum velocity is 5 m/s.