Question

If the units of length and force are increased four times each, the unit of energy is increased

• A. $4$ times
• B. $16$ times
• C. $8$ times
• D. no increase

Answer 1

The correct option is B

$16$ times

Step 1: Given data

Units of length and force are increased four times each.

Step 2: To find

The increase in the unit of energy.

Step 3: Calculation

Unit of energy$=kg{m}^2{s}^{-2}$

Unit of force$=kgm{s}^{-2}$

Unit of length$=m$

Unit of energy in terms of a unit of force and length$=\left(kgm{s}^{-2}\right)\times \left(m\right)$

If the units force and length are increased four times,

The new unit of force$=4kgm{s}^{-2}$

The new unit of length$=4m$

So, the new unit of energy$=\left(4kgm{s}^{-2}\right)\times \left(4m\right)=16kg{m}^2{s}^{-2}$

The new unit of energy is $16$ times the initial unit of energy.

So, the unit of energy is increased $16$ times.

Hence, option B is correct.