Question

The pulley and string are ideal. Tension in string T is
(a)2mg/3
(b)3mg/2
(c)4mg/3
(d) Tension in left part is mg and that in right part is 2 mg.

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Answer 1

Given:

• A pulley and mass system is provided.

To find:

• Value of tension T in the strings?

Calculation:

First of all ,

• Since it is a single string connecting m and 2m , the tension will be equal along the whole string.

For mass 2m, we can say :

$(2m)g - T = (2m)a$

For mass m , we can say :

$T - mg = ma$

• Now, add the equations :

$\implies 2mg - mg = 2ma + ma$

$\implies mg = 3ma$

$\implies a = \dfrac{g}{3}$

• Now, putting value of 'g' in the equation:

$T - mg = m( \dfrac{g}{3} )$

$\implies T = mg + m( \dfrac{g}{3} )$

$\implies T = \dfrac{4mg}{3}$

So, option c) is correct ✔️