Question

If the unit of length, Mass, energy are doubled which of the following is/are correct?
$(A)$ Unit of time is doubled.
$(B)$Unit of Momentum is doubled.
$(C)$Unit of power is doubled.
$(D)$Both $(A)$and $(B)$.

Answer 1

Hint : To solve the problem we have to write down the dimensions of the term and observe the changes that happen when the units are doubled. Going to solve the problem by doing this.
In science, Dimensional Analysis is the Analysis of the combination of various physical quantities like length, Mass, time, and also Electric charge.
Mass is the amount of matter expressed in kilograms. The velocity is directly proportional to the force.

Formula Used:
Velocity=Length$ \times $ time
Force=Mass $ \times $Acceleration
Momentum=Mass $ \times $ 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 the 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 the Momentum are $ML{T^{ - 1}}$
As time and mass are Constant and the length is doubled, The momentum will be doubled
The Dimensions of the Energy are $M{L^2}{T^{ - 2}}$
As time and mass are constant and length is doubled, then the momentum will be doubled.
The Dimensions of the Power is $M{L^2}{T^{ - 3}}$
When we double the length Power becomes $4$times
Hence, the correct answer is “B” Which is the unit of momentum that is doubled.

Note:It is very important to learn the formula and units of the quantities like force, momentum, Energy, Acceleration, Velocity, and speed. We would also need to know that the force, momentum, acceleration, and velocity are vector quantities in which we have a unique direction whereas others are scalar and they are independent of direction. The Momentum is a quantity of motion in moving objects and it is measured as the product of Mass and Velocity.