Question

Two boys are playing with a ball on a levelled ground. Boy $A$ throws the ball to height of $5m$ and boy $B$ throws to height of $7m$ from the ground level. The ratio of the work done by $A$ to $B$ is ________.

• A. 1: 1
• B. 2: 3
• C. 5: 7
• D. 3: 2

Answer 1

The correct option is C

5: 7

Let mass of ball be $m$.
Acceleration due to gravity $g$.
Height attained by the ball thrown by $A$ is $5m$.
Height attained by the ball thrown by $B$ is $7m$.
The ratio of work done by both the boys is the respective change in gravitational potential energies of the ball.
Work done by $A$ = $5mg$
Work done by $B$ = $7mg$
The ratio of the work done by $A$ to $B$ = $\frac{5mg}{7mg}=5:7$