Artificial diamonds are made by subjecting graphite to high pressure of $2 \times 10^{10}$ Pa at a high temperature. Assuming that natural diamonds were formed at such high pressure within the earth, what must have been the original volume of a diamond whose mass is 210 g? The density of diamond = 3500 $k g m^{- 3}$ and its bulk modulus = $6 x 1 0^{11} {Nm}^{- 2} .$

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

60 $c m^{3}$

62 $c m^{3}$

61 $c m^{3}$

63 $c m^{3}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given B = $6 \times 10^{11} N m^{- 2}$

Mass = 210 gm

$V o l u m e, V = \frac{m a s s}{d e n s i t y} = \frac{210 \times 10^{- 3}}{3500} = 0.06 \times 10^{- 3} m^{3}$

Bulk modulus , $B = \frac{Δ P}{(\frac{- Δ V}{V})} = \frac{(Δ P) V}{- Δ V}$

$Δ V = \frac{(Δ P) V}{B} = \frac{2 \times 10^{10} (0.06 \times 10^{- 3})}{6 \times 10^{11}} = 2 \times 10^{- 6} m^{3} = 2 c m^{3}$

$o r i g i n a l v o l u m e = V + Δ V = 60 + 2 = 62 c m^{3}$

Watch 3-min video & get full concept clarity

No courses found

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test