A particle of charge q and mass m is moving with a velocity $$ - v\widehat i$$ (v $$ \ne $$ 0) towards a large screen placed in the Y - Z plane at a distance d. If there is a magnetic field $$\overrightarrow B = {B_0}\widehat k$$ , the maximum value of v for which the particle will not hit the screen is :

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is ________.

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom.The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of
$$\gamma \left( { = {{{C_p}} \over {{C_v}}}} \right)$$ are given, respectively by:

An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :