A particle of mass 1 kg is projected at an angle of `theta = pi/4` from horizontal with a muzzle velocity of 20 m/s. A long slender rod of mass 5 kg and length 30m is suspended vertically from a point at the same horizontal level as that of projection and at a distance of 60 m from the projection point.The rod can rotate freely. If collision occurs, it is perfectly inelastic. `(g =10m//s^2)`

Angular velocity of rod after collision is

Options

A. `1/(4sqrt(2))`rad/s
B. `4/(sqrt2)`rad/s
C. `4sqrt(2)` rad/s
D. zero

Answer

A

Explanation

About point O net torque of all the force on the system is zero.
`L_i = L_f " or " (30)(1)(u_x) = I_("total") , omega " or " (30)(1)[(20)/(sqrt2)] = [(1)(30)^2 + ((5)(30)^2)/(3)] omega`
`therefore omega = 3/8 xx 20/(sqrt2) xx 30/900 = 1/(4sqrt(2) (rad)/s`