If a copper wire is stretched to increase its length by \(20 \% \). The percentage increase in resistance of the wire is \(..........\%\)

The moment of inertia of a uniform cylinder of length \(l\) and radius \(R\) about its perpendicular bisector is \(I\). What is the ratio \(l/R\) such that the moment of inertia is minimum?

Two moles of helium are mixed with \(n\)  with moles of hydrogen. If \(\frac{{{C_P}}}{{{C_V}}}\, = \,\frac{3}{2}\)  for the mixture, then the value of \(n\)  is

The magnetic intensity at the centre of a long current carrying solenoid is found to be \(1.6 \times 10^3 Am ^{-1}\). If the number of turns is 8 per cm, then the current flowing through the solenoid is \(................\,A\)

The mass density of a planet of radius \(R\) varies with the distance \(r\) from its centre as \(\rho( r )=\rho_{0}\left(1-\frac{ r ^{2}}{ R ^{2}}\right) .\) Then the gravitational field is maximum at

When a coil is placed in a time dependent magnetic field the power dissipated in it is \(P\). The number of turns, area of the coil and radius of the coil wire are \(N\), \(A\) and \(r\) respectively. For a second coils number of turns, area of the coil and radius of the coil wire are \(2N\), \(2A\) and \(3r\) respectively. When the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2}\,\alpha P\). The value of \(\alpha\) is _______.

An electric dipole of dipole moment is \(6.0 \times 10^{-6}\,Cm\) placed in a uniform electric field of \(1.5 \times 10^3\,NC ^{-1}\) in such a way that dipole moment is along electric field. The work done in rotating dipole by \(180^{\circ}\) in this field will be \(.........\,mJ\)

In an experiment to verify Stokes law, a small spherical ball of radius \(r\) and density \(\rho\) falls under gravity through a distance \(h\) in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of \(h\) is proportional to : (ignore viscosity of air)