A series \(LCR\) circuit is subjected to an AC signal of \(200 \mathrm{~V}, 50 \mathrm{~Hz}\). If the voltage across the inductor \((\mathrm{L}=10 \mathrm{mH})\) is \(31.4 \mathrm{~V}\), then the current in this circuit is _______.

Two identical circular wires of radius \(20\,cm\) and carrying current \(\sqrt{2}\,A\) are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wire is \(.............\times 10^{-8}\,T\). (Take \(\pi=3.14\) )

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbitals in a plane due to magnetic field perpendicular to the plane. Let \(r_p, r_e\) and \(r_{He}\) be their respective radii, then

The initial speed of a projectile fired from ground is \(u\). At the highest point during its motion, the speed of projectile is \(\frac{\sqrt{3}}{2} u\). The time of flight of the projectile is:

In a meter bridge experiment null point is obtained at \(40\, cm\) from one end of the wire when resistance \(X\) is balanced against another resistance \(Y\). If \(X < Y\), then the new position of the null point from the same end, if one decides to balance a resistance of \(3X\) against \(Y\), will be close to .............. \(cm\)

In the reported figure, two bodies \(A\) and \(B\) of masses \(200\, {g}\) and \(800\, {g}\) are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(.....\,{rad} / {s}\) when \({k}=20 \,{N} / {m} .\)

At \(t=0\), a body of mass \(100\) g starts moving under the influence of a force \((5\hat{i}+10\hat{j})\) N. After \(2\) s its position is \((2x\hat{i}+5y\hat{j})\) m. The ratio \(x:y\) is ______.

The temperature of 1 mole of an ideal monoatomic gas is increased by \(50^{\circ} \mathrm{C}\) at constant pressure. The total heat added and change in internal energy are \(E_1\) and \(E_2\), respectively. If \(\frac{E_1}{E_2}=\frac{x}{9}\) then the value of \(x\) is _____

Two billiard balls of mass \(0.05\,kg\) each moving in opposite directions with \(10\,ms ^{-1}\) collide and rebound with the same speed. If the time duration of contact is \(t=0.005\,s\), then \(\dots N\)is the force exerted on the ball due to each other.

A particle is moving in a straight line. The variation of position ' \(x\) ' as a function of time ' \(t\) ' is given as \(x=\left(t^3-6 t^2+20 t+15\right) m\). The velocity of the body when its acceleration becomes zero is _______.

A current of \(6\, A\) enters one corner \(P\) of an equilateral triangle \(PQR\) having \(3\) wires of resistance \(2 \,\Omega\) each and leaves by the corner \(R\). The currents \(i_{1}\) in ampere is ........ .

Given below are two statements Statement \(I:\) The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement \(II\) : The resistivity of the material is independent of temperature. In the light of the above statements, choose the correct answer from the options given below

A \(72 \; \Omega\) galvanometer is shunted by a resistance of \(8 \; \Omega\). The percentage of the total current which passes through the galvanometer is \(.....\)