Why does the earth impart the same acceleration to all bodies ?

Does earth imparts equal acceleration to all bodies ? If yes why ?

Two bodies of masses, m_A and m_B , are thrown up simultaneously. With reference to this situation, which of the given statement(s) about these bodies is/are correct? I. Both bodies fall towards the earth with same acceleration. Il. The body with heavier mass falls with more acceleration. III. The acceleration of the bodies in this case is directly proportional to the mass.

Why does shaking of the earth take place?

On the pole of the Earth a body is imparted velocity v_0 directed vertically up. Knowing the radius of the Earth and the free-fall acceleration on its surface, find the height to which the body will ascend. The air drag is to be neglected.

At which height from the earth's surface does the acceleration due to gravity decrease by 75 % of its value at earth's surface ?