An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is __________

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PY 11: GATE ME 2016 Official Paper: Shift 3

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__Concept:__

Using Newton’s second law. i.e. F = ma

Where F = Net force on the body, m = mass of body and a = acceleration

**Calculation:**

Free body diagram of above mass-pulley system

\({m_1}g = 100\;N \Rightarrow {m_1} = \frac{{100}}{g} = 10.19kg\)

\({m_2}g = 200\;N \Rightarrow {m_2} = \frac{{200}}{g} = 20.38kg\)

Consider block of 100 N:

**From Newton’s 2 ^{nd} law**

T - 100 = m_{1}a

∴ T = 10.19 a + 100 **…i)**

Now, Consider block of 200 N:

∴ 200 - T = m_{2}a

∴ T = 200 - 20.38 a **…ii)**

**From equation i) & ii)**

10.19 a + 100 = 200 - 20.38 a

**⇒ a = 3.27 m/s ^{2}**

**Now, substituting the value of a in equation (ii)**

T = 200 - 20.38 × (3.27)