Question

An uniform block of mass $M$, height $h$ and base width $a$ is kept on a enough to prevent any slipping between inclined plane and block. The angle of inclined plane is then increased. Determine the limiting value of $\theta$ so that the block does not tip over?

• A. ${\tan }^{-1}\left(\frac{a}{2h}\right)$
• B. $2{\tan }^{-1}\left(\frac{a}{2h}\right)$
• C. ${\sin }^{-1}\left(\frac{a}{2h}\right)$
• D. ${\tan }^{-1}\left(\frac{a}{h}\right)$

Answer 1

The correct option is D ${\tan }^{-1}\left(\frac{a}{h}\right)$

Component of gravity force are $Mg\sin \theta andMg\cos \theta$

Momentum at point $P$ (take clockwise direction positive)

$Mg\cos \theta \frac{a}{2}-Mg\sin \theta \frac{h}{2}\ge 0$

$g\cos \theta \frac{a}{2}\ge g\sin \theta \frac{h}{2}$

$\frac{a}{h}\ge \tan \theta$

$\theta \le {\tan }^{-1}\left(\frac{a}{h}\right)$