Question

A block A kept on an inclined surface just begin to slide if the inclination is ${30^o}$ The block is replaced by another Block B and its found that it just begins to slide if the inclination is ${40^o}$ Choose the correct option of the following.
A. mass of A $ > $ mass of B
B. mass of A $ < $ mass of B
C. mass of A $ = $ mass of B
D. all the three are possible.

Answer 1

Hint: In order to solve this question, we have to know about the concept of coefficient of friction between two objects and their relation between angle of inclination, here we will discuss about this concept and later figure out whether sliding on a body in inclined plane is depend upon the mass of the body or not.

Complete step by step answer:
As we know, that frictional force is the force which acts between the surface of contact between two objects and it always opposes the relative motion between two objects. Now, if a plane is inclined at some angle say $\theta $ and $\mu $ which is coefficient of friction between the plane and the object then, a general relation between inclination angle and coefficient of friction between two bodies is written as,
$\mu = \tan \theta $

Now, according to the question object A starts to slide when $\theta = {30^o}$ and at this angle the coefficient of friction has its some value like,
$\mu = \tan 30 = \dfrac{1}{{\sqrt 3 }}$
When the object A is replaced by object B, then the angle required to just sliding of object B were $\theta = {40^o}$ which leads to different value of coefficient of friction from the case when object A were placed.So, we see that the sliding of an object only depends upon the coefficient of friction between the two bodies and its independent of the mass of the body.So, the mass of body A can either be greater, lesser or even equal to the mass of body B.

Hence, the correct option is D.

Note: It should be remembered that, Coefficient of friction is the constant value between two bodies which is the ratio of resistive force acting between two bodies and the normal reaction force acting between surfaces of contact between two bodies.