A sphere is pushed on a horizontal surface suffirough for pure rolling such aftermoving a little dist. it mounts on an inclined plane. It rises to a height h1 and h2 if the inclined plane is frictionless or suffi rough respectively.Then - 1)h1>h2 2)h1

Dear Aveek

let the initial velocity of sphere is U

case 1 :  sphere is rolling

 acceleration along the inclind plane a= gsinθ/[1+ I/mr²]

I = 2/5 mr²

so a = 5/7 gsinθ

 now equation  V² =U²- 2aS

  S=U²/2a

 so  h2 =S sinθ = 0.7 U²/2g

 case 2:  sphere is not rolling

  a =gsinθ

and h1=Ssinθ = 0.5U²/2g

h2 > h1

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you the answer and detailed
solution very  quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin