Question

Two masses of $6Kg$ and $4Kg$ are connected to the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released. Take $g=10{ms}^{-2}$.

Answer 1

Since 6kg is heavier than 4 kg so it will accelerate down while 4 kg will accelerate up

So the equation of net force on 6kg is given as

$6\times 10-T=6a$

equation of net force on 4kg is given as

$T-4\times 10=4a$

now add the above two equations

$6\times 10-(4\times 10)=(6+4)\times a$

60 - 40 = 10a

a = 2$m/s^2$

So 6 kg will accelerate downwards while 4 kg will accelerate upwards

with acceleration 2 $m/s^2$

now in order to find the tension force

$T-4\times 10=4\times 2$

T = 48N

So the tension in the string is 48 N