# What is the magnitude of the acceleration of the masses?

## Two masses are connected by a weightless cord, which passes over a frictionless pulley. The masses are held stationary and then released. The acceleration due to gravity is g. Jan 13, 2018

$\frac{g}{4}$

#### Explanation:

For mass ${m}_{1}$

$T - {m}_{1} g = {m}_{1} {a}_{1}$

for mass #m_ 23

$T - {m}_{2} g = {m}_{2} {a}_{2}$

assuming the weightless cord is inextensible

${a}_{1} = - {a}_{2} = a$ then

$a = \left(\frac{{m}_{2} - {m}_{1}}{{m}_{1} + {m}_{2}}\right) g = \frac{1}{4} g$

Jan 13, 2018

g/4$\left(\frac{m}{s} ^ 2\right)$ for 5 kg it's downwards and for 3 kg it's upwards

#### Explanation:

Clearly the 5 kg will go downwards and as a result the cord will try to pull the 3 kg above.
Let tension in cord is T
So,for 5 kg we can write,
$5 g - T = 5 a$ ..1( a is the acceleration of the system)
For, 3 kg we can write,
$T - 3 g = 3 a$ ..2
Eliminating T from both we get, a= $\frac{5 g - 3 g}{5 + 3}$ m/$\left({s}^{2}\right)$
I.e $\frac{g}{4}$ m/$\left({s}^{2}\right)$