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प्रश्न
A uniform half metre-scale of weight W is balanced by a weight of 50 gf. The magnitude of weight W is :
![This diagram shows a (50\text{ cm}) rule balanced at the (29\text{ cm}) fulcrum, balancing its own weight ([W]) at (25\text{ cm}) against a (50\text{ gf}) load at (50\text{ cm}).](/images/_4:b6057def22ef48a0b3e3346483d3a52c.png)
पर्याय
22.65 gf
226.5 gf
26.25 gf
262.5 gf
MCQ
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उत्तर
262.5 gf
Explanation:
1. Identify the Distances from the Fulcrum (at 29 cm):
Distance of the scale's own weight (W) at the 25 cm mark (Anticlockwise arm)
\[ = 29 - 25 = 4\ \mathrm{cm} \]
Distance of the 50 gf weight at the 50 cm mark (Clockwise arm)
\[ = 50 - 29 = 21\ \mathrm{cm} \]
2. Apply the Principle of Moments:
\[ \text{Total Anticlockwise Moment} = \text{Total Clockwise Moment} \]
\[ W \times 4\ \mathrm{cm} = 50\ \mathrm{gf} \times 21\ \mathrm{cm} \]
\[ 4W = 1050 \]
\[ W = \frac{1050}{4} \]
\[ W = 262.5\ \mathrm{gf} \]
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