1. **Problem statement:** A body weighing 90 gm.wt is attached to a 30 cm string. It is pulled by a horizontal force and comes to equilibrium when it is 24 cm apart from the wall. We need to find the value of $T - F$ in gm.wt. 2. **Understanding the setup:** The string length $AB = 30$ cm, horizontal distance from the wall $= 24$ cm, and weight $W = 90$ gm.wt. 3. **Using Pythagoras theorem:** The vertical distance from the wall to the point where the weight acts is $$\text{vertical height} = \sqrt{30^2 - 24^2} = \sqrt{900 - 576} = \sqrt{324} = 18 \text{ cm}.$$ 4. **Forces in equilibrium:** The tension $T$ in the string has components balancing the horizontal force $F$ and the weight $W$. 5. **Resolving forces:** - Vertical component of tension balances weight: $$T \sin \theta = W = 90$$ - Horizontal component of tension balances horizontal force: $$T \cos \theta = F$$ 6. **Calculate angle $\theta$:** $$\sin \theta = \frac{\text{vertical height}}{\text{string length}} = \frac{18}{30} = 0.6$$ $$\cos \theta = \frac{24}{30} = 0.8$$ 7. **Calculate tension $T$:** $$T = \frac{W}{\sin \theta} = \frac{90}{0.6} = 150$$ gm.wt. 8. **Calculate horizontal force $F$:** $$F = T \cos \theta = 150 \times 0.8 = 120$$ gm.wt. 9. **Find $T - F$:** $$T - F = 150 - 120 = 30$$ gm.wt. **Final answer:** $T - F = 30$ gm.wt., which corresponds to option (d).