When body rolls dawn on inclined plane with velocity V0 at bottom then body has both rotational and translational kinetic energy. Therefore, by law of conservation of energy, P.E.=K.Etrans +K.Erotational =21mV02+21Iω2=21mV02+21mk2R02V02… (i) [∵I=mk2,ω=R0V] When body is sliding down then body has only translatory motion. ∴P.E.=K.Etrans =21m(45v0)2 Dividing (i) by (ii) we get P.E.P.E.=21×1625×mV0221mv02[1+R02K2]=1625=1+R02K2⇒R02K2=169 or, K=43R0.
A thick-walled hollow sphere has outside radius R_0. It rolls down an incline without slipping and its speed at the bottom is v_0. Now the incline is…
JEE Main 2012 — Physics Mechanics
2012mcqhard
A thick-walled hollow sphere has outside radius R0. It rolls down an incline without slipping and its speed at the bottom is v0. Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be 5v0/4. The radius of gyration of the hollow sphere about an axis through its centre is
Official previous-year question
Held on 26 May 2012 · Verified 6 Jul 2026.
Options
- A
3R0/2
- B
3R0/4
- C
9R0/16
- D
3R0
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