Underline the correct alternative : (a) When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered. (b) Work done by a body against friction always results in a loss of its kinetic/potential energy. (c) The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system. (d) In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.
a)
When the conservative work does positive work on the body, the change in the kinetic energy of the body is positive.
The change in the kinetic energy of the body is,
W = K 2 − K 1
So, the final kinetic energy of the body increases but the total energy of the body remains the same. The potential energy of the body decreases when the kinetic energy of the body increases.
Thus, the correct alternative is decreases. The correct statement is “When a conservative force does positive work on a body, the potential energy of the body decreases”.
b)
Kinetic energy is the energy possessed by the body by the virtue of its motion and the kinetic friction is the force that opposes the motion of the body. Hence, the work done by a body against friction always results in the loss of its kinetic energy.
Thus, the correct option is kinetic energy. The correct statement is “Work done by a body against friction always results in a loss of its kinetic energy”.
c)
The internal force that is present in the body cannot bring modification in the speed and the mass of the body. So, the rate of change of the total momentum is not affected. However, the external force that is applied on the system could bring change in either the mass of the system or the velocity of the system.
The external forces can change the momentum of the body. Hence, the rate of total momentum of a many particle system is proportional to the external forces of the system.
Thus, the correct option is external force of the system. The correct statement is “The rate of total momentum of a many particle system is proportional to the external forces of the system”.
d)
In an elastic collision, the momentum as well as the energy of the system remains conserved. So, the total kinetic energy, the total linear momentum and the total energy of the system of the two bodies do not change.
Thus, the correct options are the total kinetic energy, the total linear momentum and the total energy of the system of the two bodies. The correct statement is “In an elastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy, the total linear momentum and the total energy of the system of the two bodies”.
a)
When the conservative work does positive work on the body, the change in the kinetic energy of the body is positive.
The change in the kinetic energy of the body is,
So, the final kinetic energy of the body increases but the total energy of the body remains the same. The potential energy of the body decreases when the kinetic energy of the body increases.
Thus, the correct alternative is decreases. The correct statement is “When a conservative force does positive work on a body, the potential energy of the body decreases”.
b)
Kinetic energy is the energy possessed by the body by the virtue of its motion and the kinetic friction is the force that opposes the motion of the body. Hence, the work done by a body against friction always results in the loss of its kinetic energy.
Thus, the correct option is kinetic energy. The correct statement is “Work done by a body against friction always results in a loss of its kinetic energy”.
c)
The internal force that is present in the body cannot bring modification in the speed and the mass of the body. So, the rate of change of the total momentum is not affected. However, the external force that is applied on the system could bring change in either the mass of the system or the velocity of the system.
The external forces can change the momentum of the body. Hence, the rate of total momentum of a many particle system is proportional to the external forces of the system.
Thus, the correct option is external force of the system. The correct statement is “The rate of total momentum of a many particle system is proportional to the external forces of the system”.
d)
In an elastic collision, the momentum as well as the energy of the system remains conserved. So, the total kinetic energy, the total linear momentum and the total energy of the system of the two bodies do not change.
Thus, the correct options are the total kinetic energy, the total linear momentum and the total energy of the system of the two bodies. The correct statement is “In an elastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy, the total linear momentum and the total energy of the system of the two bodies”.
