A solid sphere of mass 2kg and radius 2m is rotated about its diameter with angular velocity 2rad/s.find the force exerted by one half of the sphere on the other half?

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A solid sphere of mass 2kg and radius 2m is rotated about its diameter with angular velocity 2rad/s. Find the force exerted by one half of the sphere on the other half?

To find the force exerted by one half of the sphere on the other half, we can analyze the rotational motion of the sphere and make use of Newton's second law of motion.

Step 1: Calculate the moment of inertia of the sphere
The moment of inertia of a solid sphere rotating about its diameter is given by:
I = (2/5) * m * r^2
where m is the mass of the sphere and r is the radius.
Substituting the given values, we get:
I = (2/5) * 2kg * (2m)^2
I = (2/5) * 2kg * 4m^2
I = 16/5 kg*m^2

Step 2: Calculate the torque exerted on the sphere
The torque exerted on the sphere is given by:
τ = I * α
where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
Since the sphere is rotating at a constant angular velocity, the angular acceleration is zero.
Therefore, the torque exerted on the sphere is also zero.

Step 3: Apply Newton's second law of motion
According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration.
Since the torque exerted on the sphere is zero, there is no angular acceleration, and hence no net force acting on the sphere.

Therefore, the force exerted by one half of the sphere on the other half is zero.

Conclusion:
The force exerted by one half of the sphere on the other half is zero. This is because the sphere is rotating at a constant angular velocity, and there is no angular acceleration or net force acting on the sphere.

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