A uniform rod of length ℓ receives an impulse perpendicular to its length at a point a distance x from its centre, as shown. What is the distance of the instantaneous centre of rotation from the rod centre immediately after the impulse?

Question

G1 Physics · Accepted Answer

Impulse J applied at distance x from the rod centre gives V of CM=J/m and angular speed ω=Jx/I, with I=mℓ²/12. The instantaneous centre lies at distance y=V of CM/ω from the centre. Hence y=[J/m]/[12Jx/(mℓ²)]=ℓ²/(12x). Therefore option B.