Question

If the unit of length is doubled, unit of time is halved
and unit of moment is quadrupled, the unit of work
would change by ...... times.

a) 1/8
b) 1/16
c) 16
d) 8​

Answer 1

In the question, it's given that the unit of linear momentum is quadrupled.

We know,

Work = Force × Displacement

And by the second law of motion we know that the force is the rate of change of linear momentum.

So,

Work = (Change in linear momentum) × Displacement / Time.

Hence the dimension,

[Work] = [Linear momentum] × [Displacement] / [Time]

and so is the unit.

Now, as given in the question, in the RHS,

4[Linear momentum] × 2[Displacement] / {[Time] / 2}

=> 16 [Linear momentum] × [Displacement] / [Time]

This implies that the unit of work is changed by 16 times.