An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

Muon ($$\mu $$^$$-$$) is a negatively charged (|q| = |e|) particle with a mass m_{$$\mu $$} = 200 m_e, where m_e is the mass of the electron and e is the electronic charge. If $$\mu $$^$$-$$ is bond to a proton to form a hydrogen like atom, identify the correct statements.
(A)   Radis of the muonic orbit is 200 times smaller than that of the electron.
(B)   The speed of the $$\mu $$^$$-$$ in the n^th orbit is $${1 \over {200}}$$ times that of the electron in the n^th orbit.
(C)   The ionization energy of muonic atom is 200 timesmore than of an hydroen atom.
(D)   The momentum of the muon in the n^th orbit is 200 times more than that of the electron.

The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49 $$\mu $$H and a capacitance of 2.5 nF. It is modulated by an audio signal of $$12$$ $$kHz.$$ The frequency range occupied by the side bands is :

A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :