A uniform rod of length 0.72 m is pivoted at one end and is hanging as shown. It receives a horizontal impulse at a distance x below the pivot as shown. If impulse applied by the pivot is zero, then find the value of x (in cm).

Question

G1 Physics · Accepted Answer

If the pivot impulse is zero, the centre-of-mass momentum must equal the applied impulse: J=M V of CM. Also angular impulse about the pivot gives Jx=Iₐω, and immediately after impact V of CM=ω(L/2). Hence J=MωL/2 and Jx=(ML²/3)ω, so x=2L/3=0.48 m=48 cm.