Question:
A cubical block of side L rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high, so that the block does not slide before toppling, the minimum force required to topple the block is
A cubical block of side L rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high, so that the block does not slide before toppling, the minimum force required to topple the block is
Updated On: Jun 14, 2022
- infinitesimal
- mg/4
- mg/2
- $mg(1-\mu)$
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The Correct Option is C
Solution and Explanation
At the critical condition, normal reaction N will pass through point P. In this condition $\tau_N=0=\tau_{fr}$ (about P) the block will topple when $\tau_F > \tau_{mg}$ or $FL > (mg)\frac{L}{2}$
$\therefore F> \frac{mg}{2}$
Therefore, the minimum force required to topple the block is
$F=\frac{mg}{2}$
$\therefore F> \frac{mg}{2}$
Therefore, the minimum force required to topple the block is
$F=\frac{mg}{2}$
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Concepts Used:
System of Particles and Rotational Motion
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- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.