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# A Sphere Can Roll on a Surface Inclined at an Angle θ If the Friction Coefficient is More than 2 7 G Tan θ . - Physics

MCQ
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A sphere can roll on a surface inclined at an angle θ if the friction coefficient is more than $\frac{2}{7}g \tan\theta.$ Suppose the friction coefficient is $\frac{1}{7}g\ tan\theta.$ If a sphere is released from rest on the incline, _____________ .

#### Options

• it will stay at rest

• it will make pure translational motion

• it will translate and rotate about the centre

• the angular momentum of the sphere about its centre will remain constant

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#### Solution

it will translate and rotate about the centre

The given coefficient of friction $\left(\frac{1}{7}g\ tan\theta\right)$ is less than the coefficient friction $\left(\frac{2}{7}g\ tan\theta\right)$ required for perfect rolling of the sphere on the inclined plane.

Therefore, sphere may slip while rolling and it will translate and rotate about the centre.

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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 10 Rotational Mechanics
MCQ | Q 13 | Page 195
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