Search any question & find its solution
Question:
Answered & Verified by Expert
An equilateral prism of mass $\mathrm{m}$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $\mathrm{F}$ 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 -
Options:
Solution:
1081 Upvotes
Verified Answer
The correct answer is:
$\frac{\mathrm{mg}}{\sqrt{3}}$
The tendency of rotation will be about the point C.
For minimum force, the torque of $\mathrm{F}$ about $\mathrm{C}$ has to be equal to the torque of $\mathrm{mg}$ about $\mathrm{C}$.
$$
\therefore \quad \mathrm{F}\left(\mathrm{a} \frac{\sqrt{3}}{2}\right)=\mathrm{mg}\left(\frac{\mathrm{a}}{2}\right) \Rightarrow \mathrm{F}=\frac{\mathrm{mg}}{\sqrt{3}}
$$
For minimum force, the torque of $\mathrm{F}$ about $\mathrm{C}$ has to be equal to the torque of $\mathrm{mg}$ about $\mathrm{C}$.
$$
\therefore \quad \mathrm{F}\left(\mathrm{a} \frac{\sqrt{3}}{2}\right)=\mathrm{mg}\left(\frac{\mathrm{a}}{2}\right) \Rightarrow \mathrm{F}=\frac{\mathrm{mg}}{\sqrt{3}}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.