Answer:
Step-by-step explanation:
Using Boyles law
Boyle's law states that, the volume of a given gas is inversely proportional to it's pressure, provided that temperature is constant
V ∝ 1 / P
V = k / P
VP = k
Then,
V_1 • P_1 = V_2 • P_2
So, if we want an increase in pressure that will decrease volume of mercury by 0.001%
Then, let initial volume be V_1 = V
New volume is V_2 = 0.001% of V
V_2 = 0.00001•V
Let initial pressure be P_1 = P
So,
Using the equation above
V_1•P_1 = V_2•P_2
V × P = 0.00001•V × P_2
Make P_2 subject of formula by dividing be 0.00001•V
P_2 = V × P / 0.00001 × V
Then,
P_2 = 100000 P
So, the new pressure has to be 10^5 times of the old pressure
Now, using bulk modulus
Bulk modulus of mercury=2.8x10¹⁰N/m²
bulk modulus = P/(-∆V/V)
-∆V = 0.001% of V
-∆V = 0.00001•V
-∆V = 10^-5•V
-∆V/V = 10^-5
Them,
Bulk modulus = P / (-∆V/V)
2.8 × 10^10 = P / 10^-5
P = 2.8 × 10^10 × 10^-5
P = 2.8 × 10^5 N/m²