Question

Question: Which of the following statements about the velocity and momentum of an object are correct? (1) The momentum of an object is always in the same direction as its velocity (2) The momentum of an object can be either in the same direction as its velocity or in the opposite direction. (3) The momentum of an object is perpendicular to its velocity. (4) The direction of an object's momentum is not related to the direction of its velocity. (5) The direction of an object's momentum is tangent to its path.

Short answer

Answer

Statements (1) and (5) are correct about the velocity and momentum of an object.

Step-by-step solution

Definition of the momentum

Momentum is defined as the product of mass of the particle and its velocity. It is a vector Quantity.It is given by${}_{\mathbf{p}\mathbf{=}\mathbf{m}\mathbf{v}}$here localid="1657711016505" ${}_{\mathit{P}}$is momentum, localid="1657711036356" ${}_{\mathbf{m}}$is the mass of particle and${}_{\mathit{v}}$is the velocity.

Analyzing statement (1)

This statement is correct. Since, the momentum vector is mass times the velocity vector, their directions are always same. Hence the statement (1) is correct.

Analyzing statement (2)

Direction of momentum and velocity can never be in opposite directions. It is always same. Hence the statement (2) is incorrect.

Analyzing statement (3)

The angle between direction of momentum and velocity must be zero. They can never be perpendicular to each other. Hence the statement (3) is incorrect.

Analyzing statement (4)

Direction of an object’s momentum is always related to direction of its velocity. In fact, their direction is always same. Hence the statement (4) is incorrect.

Analyzing statement (5)

The direction of instantaneous velocity is tangent to its path. Therefore, direction of momentum is always tangent to its path. Hence the statement (5) is correct.

Thus, out of all, only (1) and (5) are the correct statements.