A gold ring set with a diamond weighs 5g in air and 4.5g in water. The relative density of gold and diamond are 19.3 and 3.5 respectively. Determine the weight of the diamond

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Solution

Dear student,
Find the answer to your query as under:

mass of ring in air = 5g
mass of ring in water = 4.5g
mass of the water displaced = 0.5 g

now,
the volume of the water displaced = mass/density = 0.5/1 = 0.5 cm³
according to Archemedes principle

volume of water displaced = volume of the body submerged in the water
volume of the ring = volume of water displaced = 0.5 cm³

now,

$l e t t h e m a s s o f t h e g o l d i s' x' . t h e n t h e m a s s o f d i a m o n d = 5 - x n o w, v o l u m e o f r i n g = v o l u m e o f d i a m o n d + v o l u m e o f g o l d 0.5 = \frac{x}{19.3} + \frac{5 - x}{3.5} 33.775 - 96.5 = - 15.8 x x = 3.96 g m a s s o f d i a m o n d = 5 - 3.96 = 1.04 g$
weight of the diamond = 1.04 × g = 1.04 × 981 = 1020.24 dynes

Regards
Satyendra Singh

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