A uniform rod of mass m and length ℓ is in gravity-free space. A perpendicular impulse J is applied at distance ℓ/4 from its centre C. Point A is at distance ℓ/3 from C. Which option correctly gives the speeds of (i) C, (ii) A, (iii) the upper end and (iv) the lower end immediately after the impulse?

Question

G1 Physics · Accepted Answer

The impulse gives velocity of CM = J/m. Angular impulse about C is J(ℓ/4)=Iω with I=mℓ²/12, so ω=3J/(mℓ). Velocity of any point equals velocity of CM plus ω⃗×r⃗. Using rₐ=ℓ/3 and the end distances gives: centre J/m, point A zero, upper end J/(2m), lower end 5J/(2m). Hence option C.