Question

A horizontal circular platform of radius 0.5 m and mass axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of `9ms^(-1)` with respect to the ground. The rotational speed of the platform in `rad s^(-1)` after the balls leace the platform is

A. `4`
B. `3`
C. `2`
D. `1`

Answer 1

Correct Answer - A
Here, `R = 0.5m, M =0.45 kg`
`m = 0.05 kg, t = 0.25 m`
`upsilon = 9 m//s, omega = ?`
As is clear from Fig.

Angular momentum
`I omega = 2 m upsilon xx r`
`((1)/(2)MR^(2)) omega = 2m upsilon xx r`
`omega = (4m upsilon xx r)/(MR^(2))`
`omega = (4 xx 0.05 xx 9 xx 0.25)/(0.45 xx (0.5)^(2)) = 4 rad//sec`