The unit of length, velocity and force are doubled. Which of the following is the correct change in the other units?
A. Unit of time is doubled
B. Unit of mass is doubled
C. Unit of momentum is doubled
D. Unit of energy is doubled

- Hint: To solve this problem, you have to write down the dimensions of the term and observe the change that happens when the units are doubled. Doing this is going to solve your problem.

Formula used – Velocity = Length on Time, Force = Mass x Acceleration, Momentum = Mass x Velocity.

Complete step-by-step solution -

The dimensions of velocity are $L{T^{ - 1}}$.
The dimensions of the velocity are Since the length is doubled, there must be no change in time in the velocity to make it double.

The dimensions of force are $ML{T^{ - 2}}$.
The dimensions of the velocity are Since the length is doubled, there must be no change of time in the velocity to make it double.

The dimensions of momentum are $ML{T^{ - 1}}$.
As time and mass are constant and the length is doubled, the momentum will be doubled.

The dimensions of energy are $M{L^2}{T^{ - 2}}$.
As time and mass are constant and length is doubled, the momentum will be doubled.

Hence the correct option is C, momentum is doubled.

Note – It is very important to learn the formulas and units of the quantities like force, momentum, energy, acceleration, velocity and speed. Students should also need to know that force, momentum, acceleration and velocity are vector quantities which have a unique direction whereas others are scalar and are independent of direction.