Question

A and B are two solid spheres of equal masses. A rolls down an inclined plane without slipping from a height $H$. B falls vertically from the same height. Then on reaching the ground.

• A. both can do equal work
• B. A can do more work than B
• C. B can do more work than A
• D. both A and B will have different linear speeds

Answer 1

Answer: (A), (D)

The correct options are
A both can do equal work
D both A and B will have different linear speeds

As both the spheres fall from same height they have same potential energy initially and by law of conservation of energy both the spheres will have same energy.
Because the sphere falling directly to the ground will only have translational kinetic energy its speed will be more compared to the sphere which will roll down the incline having both translational+rotational kinetic energy.
For sphere directly falling $v=\sqrt{(}2gh)$.
For sphere rolling down $v=\sqrt{(}10/7gh)$.