Rotation 5 Question 7
17. 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
(2000)
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Answer:
Correct Answer: 17. (c)
Solution:
- At the critical condition, normal reaction $N$ will pass through point $P$. In this condition, $\tau _N=0=\tau _{f r}($ about $P)$ the block will topple when
$$ \begin{array}{cc} & \tau _F>\tau _{m g} \quad \text { or } \quad F L>(m g) \frac{L}{2} \\ \therefore \quad & F>\frac{m g}{2} \end{array} $$
Therefore, the minimum force required to topple the block is
$$ F=\frac{m g}{2} $$
