A uniform rod of mass m and length l is struck at an end by a force F perpendicular to the rod for a short time interval t. Calculate
a. the speed of the centre of mass ,b. the angular speed of the rod about centre of mass, c. the kinetic energy of the rod and d. the angular moment of the rod about the centre of mass after the force has stopped to act. Assume that t is so small that the rod does not apreciably change its direction while the force acts.

Answer

A, B, C, D

Explanation

A uniform rod of mas m and length l is truck at an end.
`rarr v=(Ft)/m`
b. the angular speed about the centre of mass
`Iomega=rxxp`
`implies ((ml^2)/12)xxomega=(l/2)xmv`
`implies (ml^2)/12xxomega=(l/2)xxFt`
`rarr omega=6Ft/ml`
c. K.E. `=1/2mv^2+1/2Iomega^2`
`=1/2xxm((Ft)/m)^2+1/2xxxIomega^2`
`=1/2xxm((F^2t^2)/m^2)+1/2xx(ml^2)/12(36)xx((F^2t^2)/(m^2l^2))`
`=(2F^2t^2)/m`
d. Angular momentum about the centre of mass
`L=mvr`
`=mxx(Ft)/mxx(l/2)=(Flt)/2`