Question

A ball of mass $0.2$ kg is thrown vertically upwards by applying a force by hand. If the hand moves $0.2$ m while applying the force and the ball goes upto $2$ m height further, find the magnitude of the force. (Consider $g=10m/s^2$)

• A. 4 N
• B. 16 N
• C. 20 N
• D. 22N

Answer 1

Answer: (D)

22N

The velocity of the ball just when it leaves the hand is $u$; then applying,

$v^2-u^2=2as$ for upward journey

where final velocity of the ball $v=0$

$\Rightarrow -u^2=2(-10)\times 2$

$\Rightarrow u^2=40$

Again applying $v^2-u^2=2as$ for the upward journey of the ball, when the ball is in the hands of the thrower,

$v^2-u^2=2as$

where initial velocity of the ball $u=0$

$\Rightarrow 40-0=2\left(a\right)0.2$

$\Rightarrow a=100m/s^2$

$\therefore f=ma=0.2\times 100=20N$

$\Rightarrow F-mg=ma=20$ where $F$ is the applied force

$\Rightarrow F=20+2=22N$

Alternatively,

$W_{hand}+W_{gravity}=\Delta K$

$\Rightarrow F\left(0.2\right)+\left(0.2\right)\left(10\right)\left(2.2\right)=0$

$\Rightarrow F=22N$