The frequency of fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of length of closed pipe to that of open pipe is

The plates of a parallel plate capacitor are separated by a distance 'd' with air as the medium between them. A dielectric slab of dielectric constant 3 is introduced between the plates so as to increase the capacity by $50 \%$. The thickness of the dielectric slab is

Two particles of equal mass ' $m$ ' move in a circle of radius ' $r$ ' under the action of their mutual gravitational attraction. The speed of each particle will be ( $\mathrm{G}=$ Universal gravitational constant)

Four particles each of mass M are placed at the corners of a square of side $L$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is