Question

Three equals weights of mass $m$ each are hanging on a string passing over a fixed pulley as shown is Fig. What are the tensions is the string connecting weight $A$ and $B$ to $C$?

• A. $7/4mg:3/4mg$
• B. $7/3mg:4/3mg$
• C. $4/3mg:2/3mg$
• D. $3/4mg:mg/4$

Answer 1

The correct option is C $4/3mg:2/3mg$

Given that,

Mass =$m$

Let, the acceleration of the system is a

For mass A

$T_1-mg=ma...\left(I\right)$

For mass B

$2mg-T_1=2ma....\left(II\right)$

For mass C

$mg-T_2=ma.....\left(III\right)$

Now, from equation (I), (II) and (III)

$2mg-T_2=ma$

$T_2=-4ma+2mg$

Now, put the value of $T_2$in equation (III)

$mg+4ma-2mg=ma$

$-mg=-3ma$

$a=\frac{g}{3}$

Now, put the value of a in equation (I)

$T_1=m\times \frac{g}{3}+mg$

$T_1=\frac{4mg}{3}$

Now, the tension $T_2$ is

$-T_2=m\times \frac{g}{3}-mg$

$T_2=\frac{2mg}{3}$

Hence, the tension is $\frac{4mg}{3}$ and $\frac{2mg}{3}$