# Two Uniform Solid Spheres Having Unequal Masses and Unequal Radii Are Released from Rest from the Same Height on a Rough Incline. If the Spheres Roll Without Slipping, - Physics

MCQ

Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping, ___________ .

#### Options

• the heavier sphere reaches the bottom first

• the bigger sphere reaches the bottom first

• the two spheres reach the bottom together

• the information given is not sufficient to tell which sphere will reach the bottom first

#### Solution

the two spheres reach the bottom together

Acceleration of a sphere on the incline plane is given by

$a = \frac{g\sin\theta}{1 + \frac{I_{COM}}{m r^2}}$

$I_{COM}$ for a solid sphere $= \frac{2}{5}m r^2$

$So, a = \frac{g\sin\theta}{1 + \frac{2m r^2}{5m r^2}} = \frac{5}{7}g\sin\theta$

a is independent of mass and radii; therefore, the two spheres reach the bottom together.

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 10 Rotational Mechanics
MCQ | Q 9 | Page 195