A body of mass \(1\,kg\) collides head on elastically with a stationary body of mass \(3\,kg\). After collision, the smaller body reverses its direction of motion and moves with a speed of \(2\,m / s\). The initial speed of the smaller body before collision is \(..........ms ^{-1}\)

Two uniformly charged spherical conductors \(A\) and \(B\) of radii \(5 mm\) and \(10 mm\) are separated by a distance of \(2 cm\). If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere \(A\) and \(B\) will be .

From the \(v\) - \(t\) graph shown. the ratio of distance to displacement in \(25\,s\) of motion

The wavelength of the radiation emitted is \(\lambda_0\) when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be \(\frac{20}{x} \lambda_0\). The value of \(x\) is \(........\)

At some location on earth the horizontal component of earth’s magnetic field is \(18\times10^{-6}\,T\). At this location, magnetic needle of length \(0.12\, m\) and pole strength \(1.8\, A\,m\) is suspended from its mid-point using a thread, it makes \(45^o\) angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is

Two coils of self inductance \(L _{1}\) and \(L _{2}\) are connected in series combination having mutual inductance of the coils as \(M\). The equivalent self inductance of the combination will be ...............

The equivalent resistance between points \(A\) and \(B\) in the given network is ............ \(\Omega\)

A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is :