Question

Let a uniform cubical block of side length 'a' is placed on a rough inclined
plane having coefficient of friction root 3 as shown

(A) for theta= 43° Rotational equilibrium will be disturbed
(B) For theta= 56° Rotational equilibrium will be disturbed
(C) For theta = 42° translational equilibrium will be disturbed
(D) All the forces acting on the block must be concurrent in the case of equilibrium
​

Answer 1

Answer:

(A) for theta= 43° Rotational equilibrium will be disturbed (B) ... (C) For theta = 42° translational equilibrium will be disturbed (D) All the forces acting on the block must be concurrent in the case of equilibrium ​ ... having coefficient of friction root 3 as shown(A) for theta= 43° Rot

Explanation:

Answer 2

Given:

Let a uniform cubical block of side length 'a' is placed on a rough inclined plane having coefficient of friction √3.

To find:

Correct statement among the following?

Calculation:

For translation equilibrium to be lost, let the minimum angle of inclination be $\theta$.

So, at critical conditions:

$\therefore \: mg \sin( \theta) = \mu mg \cos( \theta)$

$\implies \: \sin( \theta) = \mu \cos( \theta)$

$\implies \: \tan( \theta) = \mu$

$\implies \: \tan( \theta) = \sqrt{3}$

$\implies \: \theta = {60}^{ \circ}$

So, angle of inclination has to be atleast 60° in order to lose translational equilibrium.

For rotational equilibrium to be lost, the block mast topple under gravitational torque on the the inclined plane.

• Kindly remember the following relationship between minimum angle of inclination and toppling condition :

• Let the length of cube x and height of cube be y ;

$\therefore \: \tan( \phi ) = \dfrac{x}{y}$

$\implies \: \tan( \phi ) = \dfrac{a}{a}$

$\implies \: \tan( \phi ) = 1$

$\implies \: \phi = {45}^{ \circ}$

So, angle of inclination has to be at least 45° in order to lose rotational equilibrium.

OPTION B ) is correct as 56° angle of inclination can cause toppling and result in laws of rotational equilibrium.