question_answer

Direction: Question are Assertion - Reaction type. Each of these contains two statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:

Statement I: Angle of repose is equal to the angle of limiting friction.

Statement II: When the body is just at the point of motion, the force of friction in this stage is called limiting friction.

A)  Statement I is true; Statement II is true: Statement II is not a correct explanation of Statement I.

B)  Statement I is true; Statement II is false.

C)  Statement I is false; Statement II is true.

D)  Statement I is true; Statement II is true; Statement II is the correct explanation for Statement I.

Correct Answer: A

Solution :

At the point of a rough contact where stopping is about to occur the two forces acting on each object are normal reaction N and frictional force \[\mu N\]. Thus, limiting angle \[\tan \lambda =\frac{\mu N}{N}=\mu \]or\[\lambda ={{\tan }^{-1}}(\mu )\]                  ?(i) Now, at the point of sliding down the angle of inclination of the plane with the horizontal is called the angle or repose (\[\alpha \]). From figure \[\mu mg\cos \alpha =mg\sin \alpha \]             or         \[\tan \alpha =\mu \]             or         \[\alpha ={{\tan }^{-1}}(\mu )\]                              ?(ii) From Eqs. (i) and (ii)                         \[\lambda =\alpha \]