Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity $$\rho $$_C, $$\rho $$_T, $$\rho $$_M and $$\rho $$_A respectively. Then :

A particle of mass m with an initial velocity $$u\widehat i$$ collides perfectly elastically with a mass 3 m at rest. It moves with a velocity $$v\widehat j$$ after collision, then, v is given by :

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :

The mass density of a spherical galaxy varies as $${K \over r}$$ over a large distance ‘r’ from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as :