Question

A block of mass M, length L and height H is kept at
rest on a rough inclined plane of inclination a with
the horizontal as shown. If u is the coefficient of friction
between the block and the inclined plane, then the
block topples over if​

Answer 1

Given that,

Mass = M

Length = L

Height = H

Coefficient of friction = μ

If the block topples over about A, Then

The length will be $\dfrac{l}{2}$

For topple about the point A

The torque will be

$\Sum{\vec{\tau}}=0$

According to free-body diagram of the block,

Using the balance equation

$N\times\dfrac{l}{2}=f\times\dfrac{h}{2}$

Put the value in the equation

$Mg\cos\theta\times\dfrac{L}{2}=f\times\dfrac{H}{2}$

$f=\dfrac{LMg\cos\theta}{H}$

Hence, If the block topples before sliding

$\mu>\dfrac{L}{H}$