A body is free to rotate about an axis parallel to `y-`axis. A force of `vec(F)=(3hat(i)+2hat(j)+6hat(k))N` is acting on the body the position vector of whose point of applications is `vec(r)=(2hat(i)-3hat(j))m`. The moment of inertia of body about `y-`axis is `10kgm^(2)`. The angular acceleration of body is `:-`

Options

A. `(-1.8Hat(i)-1.2hat(j)+1.3hat(k))rad//s^(2)`
B. `-1.8hat(i)rad//s^(2)`
C. `-1.2hat(j)rad//s^(2)`
D. `-1.3hat(k)rad//s^(2)`

Answer

C

Explanation

Torque about origin experienced by body is `vec(tau)=vec(tau)xxvec(F)=(2hat(i)-3hat(j))xx(3hat(i)+2hat(j)+6hat(k))N-m=-18hat(i)-12hat(j)+13hat(k)`
Bu as the body is allowed to rotate only along y-axis, the y-coordinates of torque only causes the angular acceleration of the body. So, `alpha=(tau_(y))/(l)=(-12)/(10)hat(j)=-1.2hat(j) rad//s^(2)`