Question

A ball of mass 400 g is dropped from a height of 5 m. A boy on the ground hits the ball vertically upwards with a bat with an average force of 100 newton so that it attains a vertical height of 20 m. The time for which the ball remains in contact with the bat is [g = 10 m/s²]

विकल्प

• 0.12 s

• 0.08 s

• 0.04 s

• 0.02 s

Answer 1

0.12 s

Explanation:

The speed with which the ball strikes the bat,

v₁ = ${\displaystyle \sqrt{2g{h}_1}=\sqrt{2\times 10\times 5}}$ = 10 m/s

∴ ${\displaystyle {\overrightarrow{v}}_1}$ = – 10 m/s

The magnitude of the rebound velocity, v₂ = ${\displaystyle \sqrt{2g{h}_2}}$

= ${\displaystyle \sqrt{2\times 10\times 20}}$

⇒ v₂ = 20 m/s

∴ v₂ = 20 m/s

F = ${\displaystyle m\frac{dv}{dt}=\frac{m({\overrightarrow{v}}_2-{\overrightarrow{v}}_1)}{dt}=\frac{0.4[20-(-10)]}{dt}}$

∴ dt = ${\displaystyle \frac{0.4(20+10)}{100}}$

∴ dt = 0.12 s