A metre scale is supported on a wedge at its centre of gravity. A body of weight w is suspended from the 15 cm mark and another weight of 30 gram suspended from 71 cm mark balances it the metre scale remains perfectly horizontal. What is the weight of the body? Neglect the weight of the centre scale.

Options

A. 15 gram wt
B. 18 gram wt
C. 20 gram wt
D. 25 gram wt.

Explanation

To solve the problem, we need to analyze the forces acting on the meter scale and use the principle of moments (torque) to find the weight of the body \( w \).

### Step-by-Step Solution:

1. **Identify the positions of the weights**:
- The weight \( w \) is suspended from the 15 cm mark.
- A weight of 30 grams is suspended from the 71 cm mark.

2. **Determine the distances from the pivot point**:
- The pivot point is at the center of the meter scale, which is at the 50 cm mark.
- The distance from the pivot to the 15 cm mark is \( 50 - 15 = 35 \) cm.
- The distance from the pivot to the 71 cm mark is \( 71 - 50 = 21 \) cm.

3. **Set up the balance of moments**:
- For the scale to remain horizontal, the clockwise moments must equal the counterclockwise moments.
- The moment due to the weight \( w \) is \( w \times 35 \) (clockwise).
- The moment due to the 30 g weight is \( 30 \, \text{g} \times 21 \) (counterclockwise).

4. **Write the equation for balance of moments**:
\[ w \times 35 = 30 \times 21 \]

5. **Calculate the right side of the equation**:
\[ 30 \times 21 = 630 \, \text{g cm} \]

6. **Solve for \( w \)**:
\[ w = \frac{630}{35} \]
\[ w = 18 \, \text{g} \]

### Final Answer:
The weight of the body \( w \) is **18 grams**.

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