A hollow sphere and a solid sphere, having same mass and same radii, are rolled down on a rough inclined plane

Question

then, choose the correct option-
(a) the hollow sphere reaches the bottom first
(b) the solid sphere reaches the bottom with greater speed
(c) the solid sphere reaches the bottom with greater kinetic energy
(d) the 2 spheres will reach the bottom with the same linear momentum.

the correct answer, according to my book, is (b) option......can u explain why....? feel free to use torque, moment of inertia, etc etc....in ur explanation......

Answer 1

B - force and motion . Newton's law -mass=inertia More basic - solid sphere being heavier obviously gains greater momentum and reaches the bottom of slope first.

Answer 2

It is all about rotational inertia (RI):
The solid sphere has less (2/5mr^2) than the hollow sphere (2/3mr^2) with mass and radii being equal.

In converting potential energy into kinetic (c) is not correct because the masses are the same and therefore the kinetic energies will be the same.

But since the kinetic energy is made up of both a rotational component and translational component and the rotational motion of the solid is less (due to RI),
then the translational component of the solid will have to be higher to compensate, and therefore give a higher velocity than the hollow sphere.

So (b) is correct and (a) (c) and (d) are not correct.

Answer 3

Dont read the book anymore. None of the answer is correct. In some particular case c may be correct

If no friction involved both will arrive at same speed but solid sphere will have higher KE. Since the friction is proportional to the weight of the object none of the above is correct. the hollow body will reach first less friction with higher speed. but due to heavier weight c could be correst since KE has a mass term in it depending upon the mass ratio.

Answer 4

The hollow sphere's rotational acceleration will be less because the rotaional moment of inertia (k) of the hollow sphere is concentrated closer to the surface of the sphere. (k is larger)

If it will not spin up as quickly as the solid sphere, it's translational acceleration will also be slower.

Answer 5

An object in motion will travel in a straight line unless acted upon an outside force. A lighter object will be deflected easier than a heavier object. A heavier object will have more momentum than a lighter object. The longer amount of time the object spends on the ramp, the less detours it takes from the vector (shortest distance between two points) The heavier object will be thrown off course less.

Answer 6

(b) is right.this is because the gravitational pull of the earth is more on the solid sphere than the hollow sphere.therefore the solid sphere will reach the bottom with greatest speed.
HOPE THIS HELPED..