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Physics Question on mechanical properties of solids

Bulk modulus of water is 2×109N/m2 2\times 10^{9}N/m^{2} . The change in pressure required to increase the density of water by 0.1%0.1\% is

A

2×109N/m2 2\times 10^{9}N/m^{2}

B

2×108N/m22 \times 10^{8} N / m ^{2}

C

2×106N/m22 \times 10^{6} N / m ^{2}

D

2×104N/m22 \times 10^{4} N / m ^{2}

Answer

2×106N/m22 \times 10^{6} N / m ^{2}

Explanation

Solution

Mass == Volume ×\times density =Vd==V d= constant VΔd+dΔV=0V \Delta d +d \Delta V=0 ΔVV=−Δdd\frac{\Delta V}{V} =-\frac{\Delta d}{d} =−0.1100=10−3=-\frac{0.1}{100}=10^{-3} Bulk modulus K=−ΔpΔV/VK=-\frac{\Delta p}{\Delta V / V} Δp=−KΔVV\Delta p =-K \frac{\Delta V}{V} Δp=2×109×10−3\Delta p =2 \times 10^{9} \times 10^{-3} =2×106N/m2=2 \times 10^{6} N / m ^{2}