In an electrical circuit, a battery is connected to pass \(20\, C\) of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at \(15\, V\). The work done by the battery is ........... \(J\).

A bead of mass \(m\) stays at point \(P ( a , b )\) on a wire bent in the shape of a parabola \(y=4 Cx ^{2}\) and rotating with angular speed \(\omega\) (see figure). The value of \(\omega\) is (neglect friction)

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the charge in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from \(\mathrm{T}_1\) to \(\mathrm{T}_2\) is proportional to \(\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
Choose the correct answer from the options given below :

A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be

A source of sound emits sound waves at frequency \(f_0\). It is moving towards an observer with fixed speed \(v_s\) (\(v_s < v\), where \(v\) is the speed of sound in air). If the observer were to move towards the source with speed \(v_0\), one of the following two graphs (\(A\) and \(B\)) will given the correct variation of the frequency \(f\) heard by the observer as \(v_0\) is changed The variation of \(f\) with \(v_0\) is given correctly by

The intensity of the light from a bulb incident on a surface is \(0.22 \,W / m ^{2}\). The amplitude of the magnetic field in this light-wave is_______ \(\times 10^{-9} \,T\). (Given : Permittivity of vacuum \(\epsilon_{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \,ms ^{-1}\) )

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?

The electric field of an electromagnetic wave in free space is represented as \(\vec{E}=E_0 \cos (\omega t-k z) \hat{i}\). The corresponding magnetic induction vector will be _______.

In the given circuit diagram, the currents, \({I_1} =  - \,0.3\,A,\,{I_4} = 0.8\,A\) and \({I_5} = 0.4\,A,\) are flowing as shown. The currents \(I_2,\,I_3\) and \(I_6,\) respectively are

In a compound microscope the focal length of objective lens is \(1.2\, cm\) and focal length of eye piece is \(3.0\, cm\). When object is kept at \(1.25\, cm\) in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be

An electron with speed \(v\) and a photon with speed \(c\) have the same \(de-Broglie\) wavelength. If the kinetic energy and momentum of electron are \(E_{ e }\) and \(pe _{ e }\) and that of photon are \(E _{ ph }\) and \(p _{ ph }\) respectively. Which of the following is correct?

Consider an electrical circuit containing a two way switch \(^{\prime}{S}^{\prime}\). Initially \({S}\) is open and then \({T}_{1}\) is connected to \({T}_{2} .\) As the current in \({R}=6 \,\Omega\) attains a maximum value of steady state level, \({T}_{1}\) is disconnected from \({T}_{2}\) and immediately connected to \({T}_{3} .\) Potential drop across \({r}=3\, \Omega\) resistor immediately after \(T_{1}\) is connected to \(T_{3}\) is \(....\,V.\) (Round off to the Nearest Integer)

The amount of work done to break a big water drop of radius ' \(R\) ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be