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 $t^{th}$ 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, $W=$ $mgs$
$W\propto s$
$\therefore W_1$ $:W_2:W_3=1:3:5$