The radius of gyration of a solid sphere of radius 'R' and mass 'M' about its diameter is $K_d$ and that about a tangent of a solid sphere is $K_t$. The ratio of $K_d$ to $K_t$ is

A geostationary satellite is orbiting the earth at a height of $4R$ above the surface of the earth, where $R$ is the radius of the earth. Another satellite is orbiting the earth at a height $1.5R$ from the surface of the earth with periodic time 'T' in hour. The value of 'T' in hour is

One large soap bubble of diameter 'D' breaks into $64$ bubbles having surface tension 'T'. The change in surface energy is

The pressures inside two soap bubbles A and B are $1.02$ atmosphere and $1.04$ atmosphere respectively. The ratio of volume of bubble A to that of bubble B is (outside pressure $= 1$ atmosphere)