the given potentiometer has its wire of resistance \(10\, \Omega\). When the sliding contact is in the middle of the potentiometer wire, the potential drop across \(2\, \Omega\) resistor is -

The electric field in a region is given by \(\overrightarrow{ E }=\frac{2}{5} E _{0} \hat{ i }+\frac{3}{5} E _{0} \hat{ j }\) with \(E _{0}=4.0 \times 10^{3}\, \frac{ N }{ C } .\) The flux of this field through a rectangular surface area \(0.4 \,m ^{2}\) parallel to the \(Y - Z\) plane is ....... \(Nm ^{2} C ^{-1}\)

An electric field of \(1000\,V/m\) is applied to an electric dipole at angle of \(45^o\). The value of electric dipole moment is \(10^{-29}\, C.m.\) What is the potential energy of the electric dipole?

If momentum \((P),\) area \((A)\) and time \((T)\) are taken to be the fundamental quantities then the dimensional formula for energy is :

A coil is placed perpendicular to a magnetic field of 5000 T . When the field is changed to 3000 T in 2 s , an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m , then the number of turns in the coil is _______.

At \(300\,K\), the rms speed of oxygen molecules is \(\sqrt{\frac{\alpha+5}{\alpha}}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be (used \(\pi=\frac{22}{7}\) )

Given below are two statements: Statement \(I:\) If \(E\) be the total energy of a satellite moving around the earth, then its potential energy will be \(\frac{E}{2}\). Statement \(II:\) The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy \(E\). In the light of the above statements, choose the most appropriate answer from the options given below

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is _______. (Given \(=\) Radius of geo-stationary orbit for earth is \(4.2 \times 10^4 \mathrm{~km}\) )

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is \((a\,<\,<\,A)\)