Question

Two stones' different masses are thrown vertically upward with the same initial velocity. Which one will rise to a greater height?

Answer 1

Hint: The equation of motion for the stone has to be used to find the distance or height. From this, it will be found that the distance does not depend upon the mass of the object. The stone is thrown vertically upward so its motion will act under gravity.The gravitational equation of motion having initial velocity, acceleration, and displacement or height also have no relation with mass.

Complete step by step answer:
Two stones of different masses are thrown upward vertically with the same initial velocity. So, their motion will act upon gravity.Let, ${M_1}$ and ${M_2}$ are two masses of two stones respectively.The equation of height rise for \[1st\] stone is,
${H_1} = ut - \dfrac{1}{2}g{t^2}$
And, The equation of height rise for \[2nd\] stone is,
${H_2} = ut - \dfrac{1}{2}g{t^2}$
Where, $u = $ initial velocity (same for two stones), $g = $ acceleration due to gravity and $t = $ time.
From the relations, it is clearly being seen that there is no dependency of the height rise of the stones upon their masses.

Hence, it is concluded that if Two stones' different masses are thrown vertically upward with the same initial velocity, both will rise at the same height.

Note: The equation of the final velocity of each stone for the above problem will be, $v = u - gt$ , which is also independent of the mass of the stone. Again, another equation of motion for the stone that is thrown vertically upward is like, ${v^2} = {u^2} - 2gh$ , where the stone rises at the height $h$, also independent of mass.