Question

A ball is released from the top of a tower. The ratio of work done by the force of gravity in 1^st second, 2^nd second and 3^rd second of the motion of the ball is

• A. $1:2:3$
• B. $1:4:16$
• C. $1:3:5$
• D. $1:9:25$

Answer 1

Answer: (C)

Initial velocity of ball is zero ie., $ \, u=$ $0$
$\therefore $ Displacement of ball in $t^{t h}$ second
$s=gt-\frac{1}{2}g=$ $g\left(t - \frac{1}{2}\right)$
$s \propto \left(t - \frac{1}{2}\right)$
or $s_{1}:s_{2}:s_{3}=\left(1 - \frac{1}{2}\right):\left(2 - \frac{1}{2}\right):\left(3 - \frac{1}{2}\right)$
$=1:3:$ $5$
Now, $W=$ $mgs$
$W \propto s$
$\therefore W_{1}$ $:W_{2}:W_{3}=1:3:5$