Question

Which statement are not correct:
a) A body can have momentum without kinetic energy.
b) The relative velocity of the two particles in head on collision is unchanged both in magnitude and direction.
c) Potential energy of an object can have negative value.
d) Kinetic energy of an object can have negative value.
A) a, c, d
B) a, b, c
C) a, b, d
D) a, b, c, d

Answer 1

Kinetic energy of an object is the energy that it possesses due to its motion. Potential energy of an object is conserved or stored in an object.
Mathematically Kinetic energy is given as: $\dfrac{1}{2}m{v^2}$ (m is the mass and v is the velocity)
With the help of above definitions we will discuss each of the options to check whether it is correct or not.

Complete step by step solution:
a) A body can have momentum without kinetic energy.
An object cannot have momentum without having kinetic energy. If it has a non zero velocity, it has non zero kinetic energy. When there is no velocity in a body no kinetic energy is being possessed by a body and hence no momentum does exist in a body.
Statement is not correct.

b) The relative velocity of the two particles in head on collision in unchanged both in magnitude and direction.
When elastic collision is encountered between two bodies their kinetic energies will remain same but the relative velocities reverses its direction having magnitude same.
Statement is not correct.

c) Potential energy of a body can have negative value.
Yes potential energy of a body can have negative value .Potential energy is a relative concept which is measured with a frame of reference such as spring in its original position has zero Potential energy, if we stretch the spring and take this length as reference of zero potential then the original length will have negative Potential energy.
Statement is correct.

d) Kinetic energy of a body can be negative.
No, Kinetic energy of the body cannot be negative because kinetic energy is directly proportional to mass and velocity of the body and mass cannot be negative, square of velocity also gives a positive value always (as per the formula of kinetic energy in hint).
Statement is not correct.

Thus, option (C) is the correct answer.

Note: The Potential energy can have various forms such as, Gravitational potential energy, Electrostatic potential energy stored in a charge, energy possessed in a compressed spring, energy stored in stretched bow, water stored in a reservoir of a Dam to generate electrical energy.