A closely wounded circular coil of radius \(5\,cm\) produces a magnetic field of \(37.68 \times 10^{-4}\,T\) at its center. The current through the coil is \(......A\). [Given, number of turns in the coil is \(100\) and \(\pi=3.14]\)

Two persons \(A\) and \(B\) perform same amount of work in moving a body through a certain distance \({d}\) with application of forces acting at angle \(45^{\circ}\) and \(60^{\circ}\) with the direction of displacement respectively. The ratio of force applied by person \(A\) to the force applied by person \(B\) is \(\frac{1}{\sqrt{x}}\). The value of \(x\) is ...... .

A transverse wave is represented by \(y=2 \sin\) \((\omega t - kx ) cm\). The value of wavelength (in \(cm\) ) for which the wave velocity becomes equal to the maximum particle velocity, will be.

Initially a gas of diatomic molecules is contained in a cylinder of volume \(V _{1}\) at a pressure \(P_{1}\) and temperature \(250\, K\). Assuming that \(25 \%\) of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature \(2000\, K ,\) when contained in a volume \(2 V _{1}\) is given by \(P _{2}\). The ratio \(\frac{P _{2}}{  P _{1}}\) is.

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of \(10 \,m\) in \(t \;s ,\) the distance travelled by the toy in the next \(t s\) will be .........\(m\)

A solid cylinder is released from rest from the top of an inclined plane of inclination \(30^{\circ}\) and length \(60\,cm\). If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is \(...........ms ^{-1}\). (Given \(g =10\,ms ^{-2}\))

A series \(LCR\) circuit is connected to an \(AC\) source of \(220\,V , 50\,Hz\). The circuit contains a resistance \(R =80\,\Omega\), an inductor of inductive reactance \(X _{ L }=70\,\Omega\), and a capacitor of capacitive reactance \(X _{ C }=130\,\Omega\). The power factor of circuit is \(\frac{ X }{10}\). The value of \(x\) is:

\(512\) identical drops of mercury are charged to a potential of \(2\, V\) each. The drops are joined to form a single drop. The potential of this drop is ......... \(V.\)

charge \(Q\) is uniformly distributed over a long rod \(AB\) of length \(L\) as shown in the figure. The electric potential at the point \(O\) lying at distance \(L\) from the end \(A\) is

A coil of area A and N turns is rotating with angular velocity \(\omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \(\vec{B}\). Magnetic flux \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :