Question

two masses 2kg and 4 kg are connected at the two ends of a light inextensible string passing over a frictionless Pulley if the masses are released then find the acceleration of the masses and the tension in the string

Answer 1

$\sf{\underline{We\:know\:that:}}$

4 kg is heavier than 2 kg.

Since 4 kg is heavier than 2 kg, so it will accelerate down, while 2 kg will accelerate up.

Equation of net force on 4 kg is given as:

$\boxed{\sf{4 \times 10 - T = 4a}}$ ${---(1)}$

Equation of net force on 2 kg is given as:

$\boxed{\sf{T - 2 \times 10 = 2a}}$ ${---(2)}$

Now,

$\sf{\underline{Adding\:the\:above\:two\:equations:}}$

$\sf{4 \times 10 - 2 \times 10 = (4 + 2) \times a}$

$\sf{40 - 20 = 6 \times a}$

$\sf{20 = 6a}$

$\sf{\frac{20}{6} = a}$

$\sf{3.33 = a}$

So,

$\boxed{\sf{a = 3.33 \: m/s ^{2}}}$

$\sf{\underline{We\:know\:that:}}$

4 kg will accelerate downwards, while 2 kg will accelerate upwards, with acceleration $\sf{3.33 \: m/s ^{2}}$.

Now,

$\sf{\underline{In\:order\:to\:find\:tension\:force:}}$

$\sf{T - 2 \times 10 = 2 \times 3.33}$

$\sf{T - 20 = 6.66}$

$\sf{T = 6.66 + 20}$

$\boxed{\sf{T = 26.66\:N}}$

$\sf{\underline{Therefore:}}$

The acceleration of the masses is $\sf{3.33 \: m/s ^{2}}$ and the tension in the string is $\sf{26.66 \: N}$.