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Chapter 6: Problem 810

What does not change in the field of central force (A) potential energy (B) Kinetic energy (C) linear momentum (D) Angular momentum

Short Answer

Expert verified
The quantity that does not change in the field of central force is the angular momentum (D), as the torque acting on the body is zero, implying constant angular momentum.

Step by step solution

01

Understand the central force field

A central force field is a force that acts along the line joining the center of two interacting bodies. For example, gravitational and electrostatic forces are central forces. Central force is generally described as F(r) = -k/r^2, where k is a constant and r is the distance between the two bodies.
02

Investigating potential energy

Potential energy in the field of central force depends on the distance between the two bodies, and it can change depending on their relative positions. If the bodies move closer or further apart, their potential energy will change. This means that option (A) is not the correct answer.
03

Investigating kinetic energy

Kinetic energy is related to the speed of the body. In the field of central force, the speed of a body can change as it moves closer or further away from the other body in the field. For example, a body moving in an elliptical orbit around another body will have different speeds at different points along the orbit. Therefore, option (B) is also not the correct answer.
04

Investigating linear momentum

Linear momentum is given by p = mv, where m is the mass and v is the velocity of a body. As mentioned earlier, the velocity of a body can change in the field of the central force, and consequently, its linear momentum can also change. Therefore, option (C) is not the correct answer.
05

Investigating angular momentum

Angular momentum is given by L = r × p, where r is the position vector and p is the linear momentum. In the field of central force, the torque acting on the body is τ = r × F(r). Since central force acts along the line joining the centers of the interacting bodies, the torque τ = 0. This implies that the angular momentum remains constant. Hence, option (D) is the correct answer. Thus, the quantity that does not change in the field of central force is the angular momentum (D).

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