A ball is released from the top of the tower. The ratio of work done by force of gravity in first, second and third second of motion of the ball is.A. 1:2:3B. 1:4:9C. 1:3:5 D. 1:5:3

To determine the ratio of work done by the force of gravity during the first, second, and third second of motion of the ball, we need to understand the relationship between work and time.

The work done by a force is given by the equation:

Work = Force x Distance

In this case, the force acting on the ball is the force of gravity, and the distance is the height from which the ball is released. Let's assume the height is 'h.'

The work done by the force of gravity is equivalent to the potential energy of the ball at a given height. So, the work done by gravity during the first second is equal to the potential energy of the ball when it has fallen to a height of 'h' after 1 second.

Similarly, the work done during the second second is equal to the potential energy of the ball when it has fallen to a height of 'h' after 2 seconds, and so on.

The potential energy of an object at a certain height is given by the equation:

Potential Energy = Mass x Gravitational Acceleration x Height

The mass of the ball and gravitational acceleration (9.8 m/s^2) are constant, so the potential energy at different heights will be proportional to the height itself.

Therefore, the ratio of work done by the force of gravity in the first, second, and third second of motion will be proportional to the heights fallen during those time intervals.

Let's calculate the heights fallen during the first, second, and third second:

Height fallen during the first second = 1/2 x Gravitational Acceleration x (Time)^2
= 1/2 x 9.8 x (1)^2
= 4.9 meters

Height fallen during the second second = 1/2 x Gravitational Acceleration x (Time)^2
= 1/2 x 9.8 x (2)^2
= 19.6 meters

Height fallen during the third second = 1/2 x Gravitational Acceleration x (Time)^2
= 1/2 x 9.8 x (3)^2
= 44.1 meters

Now, let's calculate the ratio of the heights:

Ratio = Height fallen during the first second : Height fallen during the second second : Height fallen during the third second
= 4.9 : 19.6 : 44.1
= 1 : 4 : 9

Therefore, the ratio of work done by the force of gravity in the first, second, and third second of motion of the ball is 1:4:9.

The correct option is B. 1:4:9.