A uniform rod having length $10 \sqrt{3} m$ is oscillating between positions AB and CD with uniform angular speed about an horizontal axis passing through the centre of mass as shown in figure. Due to collision with a ball the ball bounces back between A and C again and again. The ball hits the rod always normally. Assume that all collisions are perfectly elastic. $({take g=10m/s}^{2})$

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Angular speed of rod in radian per second is $\frac{π}{3}$

Maximum speed of ball is 10 m/s

The time interval between two successive collisions of ball at A is 2s

The time interval between two successive collision of ball is 1s

answer is A, B, D.

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Detailed Solution

$R a n g e = 5 \sqrt{3} m θ = 30 ° \frac{u^{2}}{g} \sin 2 θ = 5 \sqrt{3} u^{2} = \frac{(5 \sqrt{3}) g}{\sin 60 °} = 100 u = 10 m / s T = \frac{2 u \sin θ}{g} = \frac{2 \times 10 \times \frac{1}{2}}{10} = 1 s W T = \frac{π}{3} W T = \frac{π}{3} r o d / s$