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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

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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?
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APPEARS IN

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