The mass of a precious stone is specified in carat (1 carat = 3.168 grains; 1g= 15.4 grains). The total mass of a ring containing 6.0 g gold and 0.6 carat diamond is :

The mass of a precious stone is specified in carat ( $1$ carat $= 3.168$ grains; $1 g = 15.4$ grains). The total mass of a ring containing $6.0$ g gold and $0.6$ carat diamond is :

A
$3.05 k g$
B
$6.1 x 10^{- 3} k g$
C
$2.1 x 10^{- 2} k g$
D
$3.05 g$

Solution:

Mass of gold $= 6.0 g$

Mass of diamond $= 0.6 carat \times \frac{3.168 grain}{1 carat} \times \frac{1 g}{15.4 grains} = 0.1234 g$

$∴$ Total mass of ring $= 6.0 + 0.1234 g$

$= 6.1234 g \approx 6.1 g = 6.1 \times 10^{- 3} kg .$

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