A solid sphere of radius $r$ made of a soft 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, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere$\left( {\frac{{dr}}{r}} \right)$ is
$\frac{{Ka}}{{3mg}}$
$\frac{{mg}}{{3Ka}}$
$\frac{{mg}}{{ka}}$
$\frac{{Ka}}{{mg}}$
Air is streaming past a horizontal aeroplane wing such that its speed is $120\, m/s$ over the upper surface and $90\, m/s$ at the lower surface. If the density of air is $1.3\, kg/m^3$ and the wing is $10\, m$ long and has an average width of $2\, m$ , then the difference of the pressure on the two sides of the wing is ........ $N/m^2$
Water drop whose radius is $0.0015\, mm$ is falling through the air. If the coefficient of viscosity of air is $1.8 \times 10^{-5}\, kg/m-s$, then assuming buoyancy force as negligible the terminal velocity of the dorp will be
Two liquids having densities $d_1$ and $d_2$ are mixed in such a way that both have same mass. The density of the mixture is ............
What is the pressure on a swimmer $20 \,m$ below the surface of water is ..... $atm$
If the terminal speed of a sphere of gold (density $\ =\ 19.5 × 10^3\ kg/m^3$ ) is $0.2\ m/s$ in a viscous liquid (density $\ =\ 1.5 × 10^3\ kg/m^3$ ), find the terminal speed of a sphere of silver (density $\ =\ 10.5 × 10^3\ kg/m^3$ ) of the same size in the same liquid ....... $m/s$