A ring 
a disc 
, a solid sphere 
and a hollow sphere with thin walls 
, 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
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 
and
d)
All of them will have the same kinetic energy at the bottom of the incline
A ring a disc , a solid sphere and a hollow sphere with thin walls , 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
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 and
d)
All of them will have the same kinetic energy at the bottom of the incline
Question ID - 100612 | SaraNextGen Top Answer
A ring a disc , a solid sphere and a hollow sphere with thin walls , 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
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 and
d)
All of them will have the same kinetic energy at the bottom of the incline
|
A ring |
|
|
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 |
|
d) |
All of them will have the same kinetic energy at the bottom of the incline |
|
(c,d) 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, Total kinetic energy=
Where As all the bodies have the sane final total kinetic energy, their final velocities will depend upon the ratio |
radius of gyration
.Bodies with the smaller value of 
will have the greater 
and hence will reach the bottom earlier