Choose the correct statements from the following

Options

A. The general form of Newton's second law of motion is `vecF_(ext)=vecma`
B. A body can have energy and get no momentum.
C. A body having momentum must necessarily have kinetic energy.
D. The relative velocity of two bodies in a head-on elastic collision remains unchanged in magnitude and direction.

Answer

B, C

Explanation

The general form of Newton's second law is
`vecF_(ext)=(vec(dp))/(dt)=d/(dt)(vec(mv))=m(vec(dv))/(dt)+vecv(dm)/(dt)`
The form `vecF_(ext)=vec(ma)` is valid only if `(dm)/(dt)=0`, i.e., mass does not change with time. Hence, option a is incorrect.
Option b is correct because a body at rest may have potential energy yet no momentum. Option c is also correct. A body has momentum if it has mass and velocity and a body having mass and velocity must have kinetic energy. Option d is incorrect because the relative velocity remains unchanged in magnitude and gets revrsed in direction.
`v_(2)-v_(1)=-(u_(2)-u_(1))`
Hence, the correct options are b and c.