Correct Answer - Option 1 : 4000 kg/cm

^{2}
__Concept:__

Bulk modulus (K) \( = \frac{{ - {\rm{\Delta }}P}}{{\left( {\frac{{{\rm{\Delta }}V}}{V}} \right)}}\)

Where, ΔV = change in volume = V2 – V1, ΔP = change in pressure = P2 – P1

__Calculation:__

**Given:**

V1 = 0.04 m^{3} = 40000 cm3, V2 = 0.039 m^{3} = 39000 cm3, P_{1} = 100 kg/cm^{2}, P_{2} = 200 kg/cm^{2}, K = ?

ΔV = V2 – V1 = 39000 - 40000 = -10000 cm^{3},

ΔP = P2 – P1 = 100 kg/cm2.

Bulk modulus (K) \( = \frac{{ - {\rm{\Delta }}P}}{{\left( {\frac{{{\rm{\Delta }}V}}{V}} \right)}}\)

K \(= \frac{{ - \left( {200 - 100} \right)}}{{\frac{{\left( {39000 - 40000} \right)}}{{40000}}}}\)

**K = 4000 kg/cm**^{2}