Army Group X Practice Set 1

At the bottom of the p lane, the sphere has both translational and rotational kinetic energies.
Hence , total energy =

1

2

mv2+

1

2

lω2
Using the law of conservation of energy,we can write
=

1

2

mv2+

1

2

lω2=mgh..........(i)
For a solid sphere , the moment of inertia about its centre,
l=(

2

5

)mr2
From Eq. ( i ) we get

1

2

mv2+

1

2

(mr2)ω2=mgh

1

2

v2+

1

5

r2ω2=gh
v=√

10

7

gh
Hence , the velocity of the sphere at thebottom depends only on height h andacceleration due to gravity g. Both thesevalues are constants.
Therefore, the velocity at the bottomremains the same from which everinclined plane the sphere is rolled.
So , in both c a se s speed w ill be same ,but time of descent will be different.