Question

A body of mass m is in vertical motion under the influence of gravity then
A) Work will be negative and kinetic energy increase during fall
B) Kinetic energy decrease when body is projected up and work will be negative
C) Kinetic energy increase when body is projected up and work will be positive
D) Work will be positive and kinetic energy decrease during fall

Answer 1

Hint: The kinetic energy is inversely proportional to the height of the object. Direction of force and direction of motion are at an angle of ${180^\circ}$ degrees.

Complete step by step solution:
Let us consider that, work is done when we rise or lift the particle. In order to lift a mass, we have to apply an upwards force to neutral the downward force of gravity.
If the force increases the particle through a particular height $h$ then the work is done will be
$W = F \cdot r$
$W = mg \cdot h$
As the particle height increases, the kinetic energy decreases and potential energy increases after reaching the maximum height. Work done becomes negative because when a force acts opposite to the direction of motion of a particle it is called negative work.

Hence, Kinetic energy decreases when the body is projected up and work will be negative so option (B) is the correct one.

Note: When the mass of a particle is raised to the longest height, the work done is done on the particle and energy transfer take place. Moreover, a change of height leads to change to gravitational energy of the earth.