A uniform solid sphere has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axis?

The moment of inertia about central axis becomes 18 times to its original moment of inertia when its mass doubled and radius tripled, I₁ = 18I.

Explanation:

Moment of inertia of a uniform solid sphere about its central axis is given by the relation :

   ....(1)

Here I is moment of inertia, M is mass of the solid sphere and R is the radius of the solid sphere.

Now, the mass of the sphere becomes twice and radius becomes thrice i.e.

New mass of sphere = 2M

New radius of new sphere = 3R

The new moment of inertia is:

Substitute equation (1) in the above equation.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.