Question

A solid sphere of mass 2 kg and radius 5 cm is rotating at the rate of 300 rpm. The torque required to stop it in 2π revolutions is

A. 2.5×10⁴ dyne cm
B. 2.5×10⁻⁴ dyne cm
C. 2.5×10⁶ dyne cm
D. 2.5×10⁵ dyne cm

Answer 1

The torque required to stop the rotating sphere is approximately -0.6283 N·m. Option C is correct.

Step-by-step explanation:

To calculate the torque required to stop the rotating sphere, we can use the formula:

Torque = moment of inertia * angular acceleration

First, we need to calculate the moment of inertia of the sphere using the formula:

Moment of inertia of a solid sphere = (2/5) * mass * radius^2

Plugging in the given values:

Mass = 2 kg

Radius = 5 cm = 0.05 m

Moment of inertia = (2/5) * 2 kg * (0.05 m)^2 = 0.02 kg * m^2

Since the sphere is already rotating at a certain rate, we can assume that it has an initial angular velocity. To calculate the angular acceleration, we need to find the change in angular velocity:

Change in angular velocity = (final angular velocity - initial angular velocity) = (0 - 300 rpm) * 2π / 60

Plugging in the given values:

Change in angular velocity = (0 - 300 rpm) * 2π / 60 = -10π rad/s

Now, we can calculate the torque:

Torque = moment of inertia * angular acceleration = 0.02 kg * m^2 * (-10π rad/s) = -0.2π N·m = -0.6283 N·m

So, the torque required to stop the sphere is approximately -0.6283 N·m.