Question

A ball of mass 0.2 kg is thrown vertically upwards by aaplying 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 consider g = 10m/s² [AIEEE 2006] ​

Answer 1

Explanation:

Let the ball start moving with velocity u and it reaches up to a maximum height HmaxFromHmax=u22gu=√2gHmax=√2×10ms−2×2m=2√10ms−1

This velocity is supplied to the ball by the hand and initially the hand was at rest, it acquires this velocity in distance of 0.2 m

∴a=u22S=(2√10ms−1)22×0.2m=100ms−2

So upward force on the ball isF=m(g+a)=0.2kg(10ms−2+10ms−2)=22N

Answer 2

Given:

• Mass of Ball (m) = 0.2 kg
• Height of hand (h) = 0.2 m
• Ball goes (h) = 2 m
• Total height (h) = 0.2 + 2 = 2.2 m

To Find:

• Find consider g = 10m/s²?

Solution:

$\\ \bullet{\boxed{\bf\blue{ Work \ done = Difference \ in \ potential \ energy. }}}$

$\bullet{\boxed{\bf{F.S=mgh}}}$

Remark

• where S = Distance for which the Force is applied by hand

$\mapsto {\bf\large\green{S=0.2m}}$

$\mapsto{\bf\large{ F = \dfrac{mgh}{S} }} \\ \\ \mapsto{\bf\large{ \dfrac{ \cancel{0.2} \times 10 \times 2.2 }{ \cancel{0.2}} }} \\ \\ \mapsto{\boxed{\bf\large\orange{ F = 22 \ N}}}$