A bar magnet with a magnetic moment \(5.0\,Am ^2\) is placed in parallel position relative to a magnetic field of \(0.4\,T\). The amount of required work done in turning the magnet form parallel to antiparallel position relative to the field direction is \(.........\,J\)

A copper wire of length \(3\text{ m}\) is stretched by \(3\text{ mm}\) by applying an external force. The volume of the wire is \(600 \times 10^{-6}\text{ m}^3\). The elastic potential energy stored in the wire in stretched condition would be _______ J.
(Given Young modulus of copper \(= 1.1 \times 10^{11}\text{ N/m}^2\))

A spring of unstretched length \(l\) has a mass \(m\) with one end fixed to a rigid support .Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity \(v\) is

A neutron moving with a speed \('v'\) makes a head on collision with a stationary hydrogen atom in ground state . The minimum kinetic energy of the neutron for which inelastic collision will take place is....\(eV\)

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from \(420\, Hz\) to \(490\, Hz ,\) when he hears it after it gets reflected from the wall. Find the speed of the bus (in \(kmh^{-1}\)) if speed of the sound is \(330\, ms ^{-1}\).

A long solenoid with \(1000\, turns/m\) has a core material with relative permeability \(500\) and volume \(10^{3}\, {cm}^{3} .\) If the core material is replaced by another material having relative permeability of \(750\) with same volume maintaining same current of \(0.75\, {A}\) in the solenoid, the fractional change in the magnetic moment of the core would be approximately \(\left(\frac{{x}}{499}\right) .\) Find the value of \({x}\).

A \(10\,\mu C\) charge is divided into two parts and placed at \(1\,cm\) distance so that the repulsive force between them is maximum. The charges of the two parts are :

The pressure acting on a submarine is \(3 \times 10^{5}\;Pa\) at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is \(1 \times 10^{5} \;Pa\) density of water is \(10^{3}\, kg \,m ^{-3}, g =10 \,ms ^{-2}\) )

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension \(0.095 \mathrm{~J} / \mathrm{m}^2\) and density \(10^3 \mathrm{~kg} / \mathrm{m}^3\). The difference between pressure inside the bubble and atmospheric pressure is _____ \(\mathrm{N} / \mathrm{m}^2\). (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

Given the masses of various atomic particles \(m _{ p }=1.0072 u , m _{ n }=1.0087 u\) \(m _{ e }=0.000548 u , m _{ v }=0, m _{ d }=2.0141 u\) where \(p \equiv\) proton, \(n \equiv\) neutron, \(e \equiv\) electron, \(\overline{ v } \equiv\) antineutrino and \(d \equiv\) deuteron. Which of the following process is allowed by momentum and energy conservation \(?\)

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \(\mathrm{R}=2 \mathrm{~m}\). Another car approaches him from behind with a uniform speed of \(90 \mathrm{~km} / \mathrm{hr}\). When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a is _______ \(\mathrm{m} / \mathrm{s}^2\).

A capacitor of capacitance \(100\  \mu \mathrm{F}\) is charged to a potential of \(12  \mathrm{~V}\) and connected to a \(6.4 \ \mathrm{mH}\) inductor to produce oscillations. The maximum current in the circuit would be :

The time period of a satellite in a circular orbit of radius \(R\) is \(T\). The period of another satellite in a circular orbit of radius \(9 R\) is............ \(T\)