Figure shows a smooth inclined plane fixed in a car accelerating … - Vidyadip

MCQ

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:

✓
It will continue pure rolling.
B
It will slip down the plane.
C
Its linear velocity will increase.
D
Its linear velocity will slowly decrease.

✓

Answer

Correct option: A.

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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