Question

An iron ball and a cork ball of the same radius are released from the same height in vacuum. Both of them reach the ground simultaneously. Which of the following is the correct explanation of the phenomenon?
A. in vacuum, there is no resistance to the motion of balls
B. Acceleration due to gravity is independent of the mass of the falling bodies
C. Acceleration due to gravity in vacuum is independent of size of the bodies
D. Both (B) and (C)

Answer 1

Hint:Use the expression for the acceleration due to gravity on the surface of any planet. This expression gives the relation between the universal gravitational constant, mass of the planet and radius of the planet. Use the relation and examine all the statements given in options as the free falling objects fall with acceleration equal to acceleration due to gravity.

Formula used:
The expression for acceleration due to gravity \[g\] on any planet is given by
\[g = \dfrac{{GM}}{{{R^2}}}\] …… (1)
Here, \[G\] is the universal gravitational constant, \[M\] is the mass of the planet and \[R\] is the radius of the planet.

Complete step by step answer:
-We have been given that an iron ball and a cork ball are released from the same height in the vacuum. Both of these balls reach the ground at the same time.In the vacuum, any object moves downward with an acceleration equal to acceleration due to gravity on that particular planet as the only force acting on such an object is the gravitational force in the form of its weight.In the vacuum there is no resistance to the motion of the iron ball and cork ball as there is no atmosphere in the vacuum.But this statement does not give the correct explanation for why the two balls reach on the ground at the same time.Hence, the option A is incorrect.
-From equation (1), we can conclude that the value of acceleration due to gravity on the surface of any planet is dependent on the mass of the planet.Therefore, the acceleration due to gravity does not depend on the mass of the falling objects.Hence, the statement given in option B is correct.
-Also, from equation (1), we can conclude that the value of acceleration due to gravity on the surface of any planet is dependent on the radius of the planet and hence on the size of the planet.Therefore, the acceleration due to gravity does not depend on the size of the falling objects.Hence, the statement given in option C is correct.

Hence, the correct option is D.

Note:One can also solve the same question by considering the formula for the velocity of an object in a free fall. We conclude from this formula that the time of motion for the object in a free fall depends only on acceleration due to gravity and acceleration due to gravity does not depend on the mass and size of the falling objects.