Question

If the unit of length is quadrupled and that of force is doubled, the unit power increases to ___times.
(A) 8
(B) 4
(C) 2
(D) 16

Answer 1

Hint
The formula for power is given by $P = \dfrac{{F \times L}}{T}$ . So, by putting the length and the force in both the cases we can calculate the power for both the first and second cases. Then by writing the power for the second case in terms of the first, we can find the number of times the power increases.
Formula used: $P = \dfrac{{F \times L}}{T}$
where $P$ is the power, $F$ is the force, $L$ is the length and $T$ is the time.

Complete step by step answer
In the question, the length and the force are given. So from here, we can calculate the power from the formula,
$P = \dfrac{{F \times L}}{T}$
So for the first case,let the force be ${F_1}$ and the length be $L$ .
So, the power in the first case is ${P_1} = \dfrac{{{F_1} \times {L_1}}}{T}$ .
For the second case, the force is doubled, so ${F_2} = 2{F_1}$ and the length is quadrupled so, ${L_2} = 4{L_1}$ .
So the power in the second case is, ${P_2} = \dfrac{{{F_2} \times {L_2}}}{T}$
Now substituting the values of ${F_2}$ and ${L_2}$ we get,
${P_2} = \dfrac{{2{F_1} \times 4{L_1}}}{T}$
$\Rightarrow {P_2} = 8\dfrac{{{F_1} \times {L_1}}}{T}$
we know that ${P_1} = \dfrac{{{F_1} \times {L_1}}}{T}$ therefore substituting that we get,
$\Rightarrow {P_2} = 8{P_1}$
Therefore, we can see that power becomes $8$ times.
So option (A) is correct.

Additional Information
Power is the amount of energy transferred or converted per unit time. The unit of power is given by Watt which is equal to joule per second.

Note
In this question, we have used the formula of power as $P = \dfrac{{F \times L}}{T}$
We know that power is given by work done per unit time. So we write $P = \dfrac{W}{T}$ . But the work done is given by $W = F \times L$ . Hence we can write power as, $P = \dfrac{{F \times L}}{T}$ .