Question

A crane ‘P’ lifts a car upto a certain height in $1minute.$ Another crane ‘Q’ lifts the same car upto the same height in $2minutes$.

I. Crane ‘P’ consumes two times more fuel than crane ‘Q’.

II. Crane ‘P’ supplies two times more power than crane ‘Q’.

Based on the above information, identify the correct option.

• A. Statement (I) is false while statement (II) is false.
• B. Statement (I) is false while statement (II) is true.
• C. Both statements (I) and (II) are true.
• D. Both statements (I) and (II) are false.

Answer 1

The correct option is B

Statement (I) is false while statement (II) is true.

1. Both cranes ‘P’ and ‘Q’ lifts the same car to the same height. So, the mass and the displacement remains the same.
2. The work done by the cranes ‘P’ and ‘Q’ remains the same as work done is given by $W=forcexdisplacement$.
3. As the work done is the same, the fuel spent for ‘P’ and ‘Q’ remains the same.
4. Power is expressed as $P=\frac{Workdone}{Timetaken}$
5. ‘P’ does the same work in half time ($1minute$) compared to ‘Q’ ($2minutes$).
6. So, ‘P’ supplies two times more power than ‘Q’.

Therefore, statement (I) is false and statement (II) is true.

Hence, the correct option is B.