### NEET Solved Paper 2014 Question 4

##### Question: A system consists of three masses $ m _1,m _2 $ and $ m _3 $ connected by a string passing over a pulley P. The mass $ m _1 $ hangs freely and $ m _2 $ and $ m _3 $ are on a rough horizontal table (the coefficient of friction = $ \mu $ ). The pulley is frictionless and of negligible mass. The downward acceleration of mass $ m _1 $ is (Assume, $ m _1=m _2=m _3=m $ ) [AIPMT 2014]

#### Options:

A) $ \frac{g(1-g\mu )}{9} $

B) $ \frac{2g\mu }{3} $

C) $ \frac{2(1-2\mu )}{3} $

D) $ \frac{g(1-2\mu )}{2} $

## Show Answer

#### Answer:

Correct Answer: C

#### Solution:

First of all consider the forces on the blocks For the 1st block,

$ [\because ,m _1=m _2=m _3] $ $ mg-B=m\times a $ ?(ii) Let us consider 2nd and 3rd block as a system So,

$ T _1-2\mu mg,=2m\times a $ ?(i) Solving Eqs. (i) and (ii),

Þ $ ,mg-T _1=m\times a $ $ T _1-2\mu mg=2m\times a $ $ mg(1-2\mu )=3m\times a $ $ a=\frac{2}{3}(1-2\mu ) $