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 die force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s2:

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 die force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s2: (A) 4 N (B) 16 N (C) 20N (D) 22N

Tardigrade Admin · Accepted Answer

The situation is shown in figure. At initial time, the ball is at P, then under the action of a force (exerted by hand) from P to A and then from A to B let acceleration of ball during PA is a m/

s^{2}

[assumed to be constant] in upward A direction and velocity of ball at A is v m/s.
Then for PA,

v^{2} = 0^{2} + 2 a \times 0.2

F or A B, 0 = v^{2} - 2 \times g \times 2

\Rightarrow v^{2} = 2 g \times 2

From above'equations,

a = 10 g = 100 m / s^{2}

Then for PA, FBD of ball is
F - mg = ma[ F is the force exerted by hand on ball]

\Rightarrow

F = m(g + a) = 0.2(1 lg) = 22N
Alternate solution :
Using work-energy theorem

W_{m g} + w_{F} = 0

\Rightarrow - m g \times 2.2 + F \times 0.2 = 0 \Rightarrow F = 22 N

Q. 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 die force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s2:

4 N

16 N

20N

22N

Q. 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 die force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/ $s^{2}$ :