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.

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

$6*10 - T = 6a$

equation of net force on 4kg is given as

$T - 4*10 = 4a$

now add the above two equations

$6*10 - 4*10 = (6 + 4)*a$

$60 - 40 = 10 a$

$a = 2 m/s^2$

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

$T - 4*10 = 4* 2$

$T = 48 N$

So the tension in the string is 48 N

Answer 2

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