Question

Three similar spheres of mass m and radius r are moving down along three inclined planes A, B and C of similar dimensions. Sphere on inclined plane A rolls down in pure rolling, on B it partially rolls and partially slides down the plane whereas on plane C it slides down without rolling, then at the bottom of planes

• A. Velocities of all sphere are same.
• B. Velocities on A and C are same whereas that on B is less
• C. Velocities of sphere on A is least and that on C is maximum
• D. Velocities of sphere A is maximum

Answer 1

Answer: (C)

Velocities of sphere on A is least and that on C is maximum

For inclined plane A change in energy-
$Mgh=\frac{1}{2}M{v}^2+\frac{1}{2}\frac{2}{5}M{r}^2\frac{v^2}{r^2}$
or
$Mgh=\frac{1}{2}M{v}^2+\frac{1}{5}M{v}^2$
or
$gh=\frac{7}{10}{v}^2$
or
$v=\sqrt{\frac{10}{7}gh}$
Now for plane C we have
$Mgh=\frac{1}{2}M{v}^2$
or
$v=\sqrt{2gh}$
And the velocity on incline B would lie in between that of incline A and C.