A solid ball of radius 0 . 2 m and mass 1 kg lying at rest on a smooth horizontal surface is given an instantaneous impulse of 50 N s at point P as shown. The number of rotations made by the ball abou

Question

A solid ball of radius 0 . 2 m and mass 1 kg lying at rest on a smooth horizontal surface is given an instantaneous impulse of 50 N s at point P as shown. The number of rotations made by the ball about its diameter before hitting the ground is

TestHub · Accepted Answer

Impulse = change in momentum

Along vertical

$V_{V} = \frac{50 \cos 30 °^{}}{1} \frac{m}{s} = 25 \sqrt{3}$ $m s^{- 1}$

Along horizontal

$V_{H} = \frac{50 \cos 60 °}{1} \frac{m}{s} = 25$ $m s^{- 1}$

Time of flight $T = \frac{2 V_{V}}{g} = 5 \sqrt{3} s$

Also $ω = \frac{50 \times 0.2}{\frac{2}{5} m r^{2}}$ $rad s^{- 1}$

$= 625$ $rad s^{- 1}$

$2 π n = ω T$

$\Rightarrow n = \frac{ω T}{2 π} = \frac{3125 \sqrt{3}}{2 π}$

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