Question

Assertion: A crane P lifts a car up to a certain height in $1\min $. Another crane Q lifts the same car up to the same height in $2\min $. Then crane P consumes two times more fuel than crane Q.
Reason: Crane P supplies two times more power than crane Q.
(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
(B) Bothe Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
(C) Assertion is correct but Reason is incorrect.
(D) Assertion is incorrect but Reason is correct.

Answer 1

Hint:Here, you are given two cranes, crane P and crane Q. Both the cranes lift the same car at same height but the time taken for crane P is $1\min $ and that taken by crane Q is $2\min $ and you are asked to comment on the power supplied and fuel consumption of the cranes. In order to proceed, you need to consider the correct use of the word fuel in this question. Assume the powers supplied by each crane to be ${P_P}\& {P_Q}$ and find a relation between them. Accordingly, bring your answer to any of the four conclusions given above in the options.

Complete answer:
Fuel is actually the power supplied by a mechanical machine when there is conversion of heat energy to mechanical energy. Here, the fuel consumed by the cranes is equal to the power supplied by the cranes.Let the mass of the car be $m$, $g$ be the acceleration due to gravity and $h$ be the height up to which the car is lifted by the cranes.

For crane P: The work done by the crane P is equal to ${W_P} = mgh$. The power supplied by the crane will be ${P_P} = \dfrac{{{W_P}}}{t} = \dfrac{{mgh}}{1} = mgh$ and the fuel consumed will also be the same.
For crane Q: The work done by the crane Q is equal to ${W_Q} = mgh$. The power supplied by the crane will be ${P_Q} = \dfrac{{{W_Q}}}{t} = \dfrac{{mgh}}{2}$ and the fuel consumed will also be the same.

As you can see that ${P_Q} = \dfrac{{{P_P}}}{2} \to {P_P} = 2{P_Q}$, which means that the crane P consumes two times more fuel than crane Q and also crane P supplies two times more power than crane Q.Hence, both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

Hence, option A is correct.

Note: In this question, we have taken the fuel consumed equal to the power supplied by the crane, remember this. Also, you might think that since the work required in lifting the same car to the same height is the same for both the cranes, the fuel consumed will be the same. No, you have to consider the power required and relate fuel with it. Keep in mind that the power is defined as work per unit time and unit of power is Watt.