The four arms of a Wheatstone bridge have resistances as shown in the figure. A  galvanometer of \(15\, \Omega\) resistance is connected across \(BD\). Calculate the current through the galvanometer when a potential difference of \(10\, V\) is maintained across \(AC.\)

A mass of \(1\text{ kg}\) is kept on an inclined plane with \(30°\) inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of \(4\text{ m/s}\). The work done by the frictional force in time \(2\text{ s}\) is _______ J. (Take \(g = 10\text{ m/s}^2\))

The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of increase in density of material, when a pressure \(P\) is applied uniformly on all sides, will be

A block of mass \(2\,kg\) moving on a horizontal surface with speed of \(4\,ms ^{-1}\) enters a rough surface ranging from \(x =0.5\,m\) to \(x =1.5\,m\). The retarding force in this range of rough surface is related to distance by \(F =- kx\) where \(k =12\,Nm ^{-1}\). The speed of the block as it just crosses the rough surface will be ........... \(\,ms ^{-1}\)

In the Bohr model an electron moves in a circular orbit around the proton . Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom; when the electron is in \(n^{th}\) excited state, is

A point particle of charge \(Q\) is located at \(P\) along the axis of an electric dipole 1 at a distance \(r\) as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distance \(2 a\). For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

If \({q}_{{f}}\) is the free charge on the capacitor plates and \({q}_{{b}}\) is the bound charge on the dielectric slab of dielectric constant \(k\) placed between the capacitor plates, then bound charge \(q_{b}\) can be expressed as 

A body of mass \(2\, {kg}\) moving with a speed of \(4\, {m} / {s}\). makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is \(\frac{x}{10} \,{m} / {s}\). Then the value of \(x\) is ..... .

A solid sphere, of radius \(R\) acquires a terminal velocity \(\nu_1 \) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta \). The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(\nu_2\), when falling through the same fluid, the ratio \((\nu_1/\nu_2)\) equals

A particle of mass \(m\) projected with a velocity ' \(u\) ' making an angle of \(30^{\circ}\) with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height \(\mathrm{h}\) is _______.

A spherical ball of mass \(2\) kg falls from a height of \(10\) m and is brought to rest after penetrating \(10\) cm into sand. The average force exerted by sand on the ball is _______ N. (Take \(g = 10\) m/s\(^2\))

A transformer operating at primary voltage \(8\,kV\) and secondary voltage \(160\,V\) serves a load of \(80\,kW\). Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be.

Two open organ pipes of length \(60 \mathrm{~cm}\) and \(90 \mathrm{~cm}\) resonate at \(6^{\text {th }}\) and \(5^{\text {th }}\) harmonics respectively. The difference of frequencies for the given modes is _______ \(\mathrm{Hz}\). (Velocity of sound in air \(=333 \mathrm{~m} / \mathrm{s}\) )