Tension in Pulley System PYQ | JEE Main Physics 2025

 

❓ Question

In the pulley system shown, the masses are

• $2\,\text{kg}$
  
• $5\,\text{kg}$
  
• $3\,\text{kg}$
  

with

$$g=10\ \text{m/s}^2.$$

Find the tension $T_1$ in the string between the 5 kg and 3 kg masses.

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✍️ Solution

Let the acceleration of the system be $a$.

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For the $2\,\text{kg}$ Block

Applying Newton's Second Law,

$$T_2-2g=2a.$$

Substituting $g=10$,

$$T_2=2a+20.$$

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For the $3\,\text{kg}$ Block

Applying Newton's Second Law,

$$3g-T_1=3a.$$

Substituting $g=10$,

$$T_1=30-3a.$$

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For the $5\,\text{kg}$ Block

The forces acting are

• Right: $T_1$
• Left: $T_2$

Applying Newton's Second Law,

$$T_1-T_2=5a.$$

Substitute the expressions for $T_1$ and $T_2$:

$$(30-3a)-(2a+20)=5a.$$
$$10-5a=5a.$$
$$10=10a.$$
$$a=1\ \text{m/s}^2.$$

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Calculate $T_1$

$$T_1=30-3a.$$
$$T_1=30-3(1)=27\ \text{N}.$$

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✅ Final Answer

$$\boxed{T_1=27\ \text{N}}$$