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)`

If the rod tilts to an angle `theta` after collision, then

Options

A. `theta = 0^@`
B. `theta = cos^(-1)(40//41)`
C. `theta = cos^(-1)(27//28)`
D. `theta = (pi//2)`

Answer

C

Explanation

Increase in potential energy of rod and particle=Decrease in rotational kinetic energy.
`therefore (1)(10)30(1 - cos theta) + (5)(10)(15) (1 - cos theta) = 1/2[(1)(30)^2 + ((5)(30)^2)/(3)][1/(4sqrt2)]^2`
Solving this equation, we get `theta = cos^(-1)(27/28)`