## Question

Find the minimum value of 'm', for the system to be in equilibrium. Take $g = 10 \mathrm{ m/s}^{2}$.

A 10 kg

B 15 kg

C 20 kg

D 25 kg

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## Answer

The correct answer is **D) 25 kg**.

To find the minimum value of $m$ for the system to be in equilibrium, we start with the given equations:

- Given: $\mathrm{T}_2 \sin 45^\circ = 100 \mathrm{~N}$
- And: $\mathrm{T}_2 \cos 45^\circ = \mathrm{T}_1$

From these, we derive: $$ \mathrm{T}_1 = 100 \mathrm{~N} $$

Next, consider the Free Body Diagram (FBD) for the block in the limiting case: $$ \mathrm{T}_1 \leq \mathrm{f} = \mu mg = 0.4mg $$

Therefore: $$ m \geq 25 \mathrm{~kg} $$

Thus, for the system to be in equilibrium, the **minimum value of 'm'** must be **25 kg**.

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