A straight rigid rod of mass `M` and length `L` lies on a smooth horizontal table. Taking the co-ordinate axes as shown in the figure and assuming an average force `ltFgt` acting for a small time interval `(/_\t)`, at the end `A`, making an angle `30^@` with the `X`-axis, Based on the above passege, answer the following questions.
The angular impulse, due to the force about `O`, is

Options

A. `(sqrt(5))/4F(/_\t)Lhatk`
B. `(sqrt(5))/2F(/_\t)Lhatk`
C. `(sqrt(3))/4F(/_\t)Lhatk`
D. `(sqrt(3))/2F(/_\t)Lhatk`

Answer

C

Explanation

Impulse applied `J=ltFgt/_\t`
Angular impuse about O is
`J_x xxL/2=Jcos30^@xxL/2`
`=(:F:)xx/_\txxsqrt3/2xxL/2`
`=sqrt3/4(:F:)/_\xxl`

And direction is anticlock wise about O.
Hence `hatk` direction.