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Rotational Mechanics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsRotational Mechanics1 Mark
MCQ
A sphere can roll on a surface inclined at an angle $\theta$ if the friction coefficient is more than $\frac{2}{7}\text{g}\tan \theta.$ Suppose the friction coefficient is $\frac{1}{7}\text{g}\tan \theta.$ If a sphere is released from rest on the incline:
  • A
    It will stay at rest.
  • B
    It will make pure translational motion.
  • ✓
    It will translate and rotate about the centre.
  • D
    The angular momentum of the sphere about its centre will remain constant.
✓

Answer

Correct option: C.
It will translate and rotate about the centre.
The given coefficient of friction $\Big(\frac{1}{7}\text{g}\tan\theta\Big)$ is less than the coefficient friction $\Big(\frac{2}{7}\text{g}\tan\theta\Big)$ 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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