Question

In the system shown in figure pulley is smooth. String is massless and inextensible. Find acceleration of the system a, tensions $T_{1}and{T}_2.$ $(g=10m/s^2)$. Report the sum of their values.

• A. $20$
• B. $10$
• C. $20/3$
• D. $40$

Answer 1

The correct option is C $20/3$

Here, net pulling force will be:
Weight of $4kg$ and $6kg$ blocks on one side and weight of $2kg$ block on the other side.
Therefore,
$a=\frac{Netpullingforce}{Totalmass}$
$=\frac{(6\times 10)+(4\times 10)-\left(2\right)\left(10\right)}{6+4+2}$
$=\frac{20}{3}m/s^2$
For $T_1,$ let us consider FBD of $2kg$ block. Writing equation of motion, we get
$T_1-20=2a$
or $T_1=20+2\times \frac{20}{3}=\frac{100}{3}N$
For $T_2,$ we may consider FBD of $6kg$ block. Writing equation of motion, we get
$60-T_2=6a$
$T_2=60-6a$
$=60-6\left(\frac{20}{3}\right)$
$=20N$