Question

A block of weight Q rests on an inclined plane and it is attached to a string which runs over a frictionless pulley to carry a block of weight $P$ at its other end. The coefficient of friction between the block of weight Q and the inclined plane is $\mu$
consider the following cases:
Case -I: weightQ starts moving down the inclined plane
Case -II: weight P starts falling down


The limiting values of ratio $P/Q$for case I and case II respectively are

• A. $(sin\alpha -\mu cos\alpha )and(sin\alpha +\mu cos\alpha )$
• B. $(\mu sin\alpha -cos\alpha )and(\mu sin\alpha +cos\alpha )$
• C. $(sin\alpha +\mu cos\alpha )and(sin\alpha -\mu cos\alpha )$
• D. $(\mu sin\alpha +cos\alpha )and(\mu sin\alpha -cos\alpha )$

Answer 1

The correct option is A $(sin\alpha -\mu cos\alpha )and(sin\alpha +\mu cos\alpha )$

$\text{Case -I}$

$Qsin\alpha =T+\mu Qcos\alpha \to ......1$

$T=P\to ........2$

From 1 and 2

$\frac{P}{Q}=sin\alpha -\mu cos\alpha$

$\text{Case -II}$

$Qsin\alpha +\mu Qcos\alpha =T\to ........3$

$T=P\to .......4$

from 3and 4

$\frac{P}{Q}=sin\alpha +\mu cos\alpha$