Q.
A ring (R), a disc (D), a solid sphere (S) and a hollow sphere with thin walls (H), all having the same mass but different radii, start together from rest at the top of an inclined plane and roll down without slipping. Then
see full answer
Want to Fund your own JEE / NEET / Foundation preparation ??
Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*
An Intiative by Sri Chaitanya
a
all of them will reach the bottom of the incline together
b
the body with the maximum radius will reach the bottom first
c
they will reach the bottom in the order S, D, H and R
d
all of them will have the same kinetic energy at the bottom of the incline
answer is C.
(Unlock A.I Detailed Solution for FREE)
Ready to Test Your Skills?
Check your Performance Today with our Free Mock Test used by Toppers!
Take Free Test
Detailed Solution
In rolling without slipping, no work is done against friction. Hence, loss in gravitational potential energy of a body is equal to its total kinetic energy, i.e., linear plus rotational kinetic energies.Also, v=ωrTotal kinetic energy =12mv2+12Iω2=12mv2+12mK2v2r2=12mv21+K2r2where K = radius of gyrationAs all the bodies have the same final total kinetic energy, their final velocities will depend upon the ratio K/r. Bodies with the smaller value of K/r will have the greater v and hence will reach the bottom earlier.
Watch 3-min video & get full concept clarity