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: 1. The heavier sphere reaches the bottom first. 2. The bigger sphere reaches the bottom first. 3. The two spheres reach the bottom together. 4. The information given is not sufficient to tell which sphere will reach the bottom first.

3. The two spheres reach the bottom together. Explanation: Acceleration of a sphere on the incline plane is given by: a= g 1+ I_ COM mr^2 ICOM for a solid sphere =2 5 mr^2 So, a= g 1+ 2mr^2 5mr^2 =5 7 g a is independent of mass and radii; therefore, the two spheres reach the bottom together.

Two uniform solid spheres having unequal masses and unequal radii…

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Question

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:

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.

✓

Answer

The two spheres reach the bottom together.

Explanation:

Acceleration of a sphere on the incline plane is given by:

$\text{a}=\frac{\text{g}\sin\theta}{1+\frac{\text{I}_{\text{COM}}}{\text{mr}^2}}$

I_COM for a solid sphere $=\frac{2}{5}\text{mr}^2$

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

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

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