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Physics Question on mechanical properties of solids

When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01%. The bulk modulus of elasticity of the material of sphere is (Given, density of water =1gcm−3)= 1 gcm^{-3})

A

9.8×1010Nm−29.8\times10^{10}Nm^{-2}

B

10.2×1010Nm−210.2\times10^{10}Nm^{-2}

C

0.98×1010Nm−20.98\times10^{10}Nm^{-2}

D

8.4×1010Nm−28.4\times10^{10}Nm^{-2}

Answer

9.8×1010Nm−29.8\times10^{10}Nm^{-2}

Explanation

Solution

Bulk modulus B=Δp−ΔVVB=\frac{\Delta p}{\frac{-\Delta V}{V}} −ΔVV=0.01100=10−4\frac{-\Delta V}{V}=\frac{0.01}{100}=10^{-4} Δp=pressureofwater=hρg\Delta p=pressure of water=h\rho g = 103×1×10×9.810^3\times1\times10^\times9.8 Δp=9.8×106\Delta p=9.8\times10^6 B=9.8×10610−4B=\frac{9.8\times10^6}{10^{-4}} =9.8×1010Nm−2=9.8\times10^{10}Nm^{-2}