How many times more compressible are gases compared to solids?

  • A
    $10^2$ times
  • B
    $10^4$ times
  • C
    $10^6$ times
  • D
    $10^8$ times

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$A$ solid sphere of radius $R$ made of a material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. $A$ massless piston of area $A$ floats on the surface of the liquid. When a mass $m$ is placed on the piston to compress the liquid,the fractional change in the radius of the sphere $\delta R/R$ is

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The adiabatic bulk modulus of a gas at a pressure $P$ is (where $\gamma$ is the ratio of specific heat capacities of the gas).

The Mariana Trench is located in the Pacific Ocean,and at one place it is nearly $11 \; km$ beneath the surface of the water. The water pressure at the bottom of the trench is about $1.1 \times 10^{8} \; Pa$. $A$ steel ball of initial volume $0.32 \; m^{3}$ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom? (Bulk modulus of steel $B = 1.6 \times 10^{11} \; N/m^{2}$)

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