A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and anothe

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4-2.Friction

hard

A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta $ to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is

A$\frac{{(P + Q\sin \theta )}}{{(mg + Q\cos \theta )}}$

B$\frac{{(P\cos \theta + Q)}}{{(mg - Q\sin \theta )}}$

C$\frac{{(P + Q\cos \theta )}}{{(mg + Q\sin \theta )}}$

D$\frac{{(P\sin \theta - Q)}}{{(mg - Q\cos \theta )}}$

Solution

(a) By drawing the free body diagram of the block for critical condition
$F = \mu \,R$ $⇒$ $P + Q\sin \theta $
$ = \mu \,(mg + Q\cos \theta )$
$\therefore \mu = \frac{{P + Q\sin \theta }}{{mg + Q\cos \theta }}$

Standard 11

Physics

A man balances himself in a horizontal position by pushing his hands and feet against two parallel walls. His centre of mass lies midway between the walls. The coefficients of friction at the walls are equal. Which of the following is not correct?

medium

In the diagram, $BAC$ is a rigid fixed rough wire and angle $BAC$ is $60^o$. $P$ and $Q$ are two identical rings of mass $m$ connected by a light elastic string of natural length $2a$ and elastic constant $\frac{mg}{a}$. If $P$ and $Q$ are in equilibrium when $PA = AQ = 3a$ then the least coefficient of friction between the ring and the wire is $\mu$. Then value of $\mu + \sqrt 3 $ is :-

normal

What is friction ? What is impending motion ?

easy

A force of $98\, N$ is required to just start moving a body of mass $100\, kg$ over ice. The coefficient of static friction is