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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Physics
Chapter
Rotational Motion

BITSAT 2014 · Physics · Rotational Motion

An equilateral prism of mass m rests on a rough horizontal surface...

An equilateral prism of mass m\mathrm{m} rests on a rough horizontal surface with coefficient of friction μ\mu. A horizontal force F\mathrm{F} is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is - An equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction μ . A horizontal force

Options

  1. Amg3\frac{\mathrm{mg}}{\sqrt{3}}
  2. Bmg4\frac{\mathrm{mg}}{4}
  3. Cμmg3\frac{\mu \mathrm{mg}}{\sqrt{3}}
  4. Dμmg4\frac{\mu \mathrm{mg}}{4}

Correct answer

A. mg3\frac{\mathrm{mg}}{\sqrt{3}}

Step-by-step solution

The tendency of rotation will be about the point C. An equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction μ . A horizontal force
For minimum force, the torque of F\mathrm{F} about C\mathrm{C} has to be equal to the torque of mg\mathrm{mg} about C\mathrm{C}. \therefore \quad F(a32)=mg(a2)⇒F=mg3\mathrm{F}\left(\mathrm{a} \frac{\sqrt{3}}{2}\right)=\mathrm{mg}\left(\frac{\mathrm{a}}{2}\right) \Rightarrow \mathrm{F}=\frac{\mathrm{mg}}{\sqrt{3}}
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