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Question

A body of mass 1kg and 10kg are dropped simultaneously from the top of a tower. The ratio of the time taken by them to reach the ground is


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Solution

Step 1: Given data

A body of mass 1kg and 10kg are dropped simultaneously from the top of a tower

Step 2: Gravitational force

  1. When a body is dropped from a certain height then it falls freely under the influence of gravitational force acted by the earth on the body and the acceleration achieved by the body is g.
  2. Gravitational acceleration is independent of mass. It is dependent on the mass of the earth and the distance between the two bodies.

Step 3: Proving that acceleration due to the gravity of a body is independent of its mass.

If the body's mass is m and it falls freely under the effect of gravity, then according to Newton's second law. F=mg[F=force,m=mass,g=accelerationduetogravity]

This force is on account of gravitational force which is given by,

F=GMmr2[M=massofearth,r=distancebetweenbodyandearth'ssurface]

Equating both of the above two forces of the equation we get,

mg=GMmr2g=GMr2

Thus, it is clear that the value of g is independent of the mass of the body. It is dependent on the mass of the earth and the distance between the two bodies.

Step 4: Analyzing the given data

Two bodies of masses 1kg and 10kg are dropped simultaneously from the top of the tower. As we have discussed the acceleration is independent of mass and hence same time will be required.

Therefore, the ratio of the time taken by them to reach the ground is 1:1.


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