Question

Two balls of mass ratio 1:2 are dropped from the same height.
1) State the ratio between their velocities when they strike the ground.
2) The ratio of the forces acting on them during motion.

Answer 1

Hint:There is a famous experiment conducted by Galileo, he was in the church at a certain height. He was having two balls of different masses in his hand, he dropped the ball from the same height at the same time, to his amusement he noticed that the two balls irrespective of their masses reached the ground at the same time.

Complete step by step solution:
Step 1: Here, we need to see that the ratio between the masses is not very big. Here we need to ignore the air resistance and other factors that might affect the velocity of the balls. We have to consider the fact that the two balls are only under the influence of gravitational force in other words we only have to consider the gravitational force while considering the dropping of a ball at a certain height. So, when the balls are dropped at a certain height the balls solely under the influence of gravity will hit the ground at the same time. Two balls can only hit the ground at the same time if their velocities are the same and hence the ratio between the velocities of the two balls with mass ratio 1:2 is 1:1.

Step 2: Find out the ratio of the forces:
Apply Newton’s second law.
$F = ma$;
Where:
F = Force;
m = Mass;
a = Acceleration;
Force on the first ball:
\[{F_1} = {m_1} \times a\];
Force on the second
 \[{F_2} = {m_2} \times a\];
To find ratio divide\[{F_1}\]by\[{F_2}\]:
\[\dfrac{{{F_1}}}{{{F_2}}} = \dfrac{{{m_1} \times a}}{{{m_2} \times a}}\];
\[\dfrac{{{F_1}}}{{{F_2}}} = \dfrac{{{m_1}}}{{{m_2}}}\];
\[\dfrac{{{F_1}}}{{{F_2}}} = \dfrac{1}{2}\];

Final Answer:The ratio between their velocities when they strike the ground 1:1. The ratio of the forces acting on them during motion 1:2.

Note:Here we need to explain the reason for the velocities having the same ratio even when the masses are different from each other. The ratio of the forces on the two balls are different because of different masses.