Question

If the momentum of a body doubles, then its kinetic energy will:

• A. Become twice
• B. Become half
• C. Become four times
• D. Become nine times

Hint:

Kinetic energy is proportional to the square of the velocity. So, when velocity doubles, the kinetic energy increases by a factor of four.

Answer 1

The Correct Option is C

The kinetic energy (\( K.E. \)) of a body is given by the formula: \[ K.E. = \frac{1}{2} m v^2 \] where \( m \) is the mass and \( v \) is the velocity of the body. The momentum (\( p \)) of a body is given by: \[ p = m v \] If the momentum of a body doubles, the velocity of the body also doubles (since momentum is directly proportional to velocity for constant mass). Now, if the velocity is doubled, the kinetic energy will increase by a factor of: \[ K.E. \propto v^2 \] Since \( v \) is doubled, the kinetic energy becomes four times greater, as \( (2v)^2 = 4v^2 \). Thus, the kinetic energy will become four times greater when the momentum is doubled.