In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is $$t$$ second. The frequency of vibration of air column is

A particle of mass '$$m$$' is kept at rest at a height $$3 R$$ from the surface of earth, where '$$R$$' is radius of earth and '$$M$$' is the mass of earth. The minimum speed with which it should be projected, so that it does not return back is ( $$g=$$ acceleration due to gravity on the earth's surface)

'$$\mathrm{F}$$' is the force between the two identical charged particles placed at a distance '$$\mathrm{Y}$$' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes

A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is changing) so that their centres coincide. ( $$R > r$$ ). If both coplanar, then the mutual inductance between them is proportional to