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Rotational Mechanics — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsRotational Mechanics1 Mark
Question
Figure shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline 0 is related to the acceleration a of the car as a = g tan°. If the sphere is set in pure rolling on the incline:
  1. It will continue pure rolling.
  2. It will slip down the plane.
  3. Its linear velocity will increase.
  4. Its linear velocity will slowly decrease.
✓

Answer

  1. It will continue pure rolling.
Explanation:

From the free body diagram of sphere, we have:
Net force on the sphere along the incline,
$\text{F}_{\text{net}}=\text{mg}\sin\theta-\text{ma}\cos\theta\ \dots(\text{i})$
On putting $\text{a}=\text{g}\tan\theta$ in equation (i), we get:
$\text{F}_{\text{net}}=0$
Therefore, if the sphere is set in pure rolling on the incline, it will continue pure rolling.

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