Question

A hollow iron ball (A) and a solid iron ball (B) and a cricket ball (C) are dropped from the same height. Which among the three balls reaches the ground first? Assuming there is no resistance due to air.
(A) A
(B) B
(C) C
(D) All the three balls reach ground simultaneously.

Answer 1

Hint: Use the fourth kinematical equation. Also, the initial velocity of any dropped object is zero. Recall the phenomenon of acceleration due to gravity.

Complete step by step answer:
Since the three balls dropped from the same height, the initial velocity of the balls is zero.
Now, the only force acting on the balls is the gravitational force since we have neglected the air resistance. The acceleration produced due to the gravitational force is the acceleration due to gravity. The acceleration due to gravity does not depend upon the mass of the object. Therefore, the acceleration produced in (A), (B), and (C) is the same.
We can use the fourth kinematical equation to answer this question.
The fourth kinematical equation relates displacement, initial velocity, acceleration and time. It is given by the equation,
\[s = ut + \dfrac{1}{2}a{t^2}\]
Here, s is the displacement, u is the initial velocity of the body, a is the acceleration and t is the elapsed time.
Since the initial velocity for all three balls is zero, the above equation becomes,
\[s = \dfrac{1}{2}a{t^2}\]
\[ \Rightarrow t = \sqrt {\dfrac{{2s}}{a}} \]
Here, s is the distance between initial and final position of the balls.Since the distance s is the same for all three balls, the time required to reach the ground depends upon only the acceleration due to gravity.
Therefore, the balls (A), (B), and (C) will reach the ground simultaneously.
So, the correct answer is option (D).

Note: Here we have neglected the air resistance which creates buoyant force and acts in the upwards direction of the motion for the falling body. One can also refer to Newton’s law of gravitation to answer this question. Since the mass of the earth is very large as compared to the mass of the object, the gravitational force is the same for all the three balls.