Question

An iron sphere having mass $10kg$ and aluminium sphere have mass $3.5kg$. They both have the same diameter and are dropped at the same time from a tower. When they are $10m$ above the ground, they have same
(A) Acceleration
(B) momenta
(C) potential energy
(D) kinetic energy

Answer 1

Hint
During free fall of an object from a height above the ground the acceleration of the object becomes equal to acceleration due to gravity which is equal to $9.8m{s^{ - 2}}$.
It is given that aluminium sphere and iron sphere have different masses.

Complete step by step answer
The acceleration which is gained by an object due to gravity is called acceleration due to gravity. The S.I unit of acceleration due to gravity is $m{s^{ - 2}}$. It is a vector quantity because it has magnitude and direction both. It is denoted by $g$ and is equal to $9.8m{s^{ - 2}}$.
Let the mass of the aluminium sphere and iron sphere be ${M_a}$ and ${M_i}$ respectively.
 According to question, it is given that
Mass of aluminium sphere, ${M_a} = 3.5kg$,
Mass of iron sphere, ${M_i} = 10kg$.
When the object falls from a height above the ground the acceleration becomes equal to the acceleration due to gravity and becomes independent of mass.
Therefore, acceleration of both spheres will be equal to $9.8m{s^{ - 2}}$.
We know that,
Kinetic Energy $ = \dfrac{1}{2}M{v^2}$
Also, Potential energy $ = Mgh$
Also, Momentum $ = Mv$
Kinetic energy, potential energy and momentum all of them depend upon mass which is not the same for both spheres which will make the values of these three different with respect to the spheres.
Therefore, acceleration is the only one which is the same for both spheres.
Hence, option (A) is correct.

Note
The value of acceleration due to gravity is more at equator and less at poles. Its value decreases when the depth increases.
Mathematically, the formula for acceleration due to gravity is-
$g = G\dfrac{M}{{{r^2}}}$.