Figure shows a circuit that contains four identical resistors with resistance \(R =2.0\, \Omega,\) two identical inductors with inductance \(L =2.0 \,mH\) and an ideal battery with \(e m f E =9 \,V .\) The current \('i'\) just after the switch \('S'\) is closed will be .... \(A\)

A rolling wheel of \(12 \,kg\) is on an inclined plane at position \(P\) and connected to a mass of \(3 \,kg\) through a string of fixed length and pulley as shown in figure. Consider \(PR\) as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom \(Q\) of the inclined plane \(P Q\) will be \(\frac{1}{2} \sqrt{ xgh } \,m / s\). The value of \(x\) is.............

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point \(B\) with respect to the point \(A\) is\(.......V\)

A passenger train of length \(60\, m\) travels at a speed of \(80\, km/hr\). Another freight train of length \(120\, m\) travels at a speed of \(30\, km/hr\). The ratio of times taken by the passenger train to completely cross the freight train when: \((i)\) they are moving in the same direction, and \((ii)\) in the opposite directions is

Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror \((M_1)\) and parallel to the second mirror \((M_2)\) is finally reflected from the second mirror \((M_2)\) parallel to the first mirror \((M_1).\) The angle between the two mirrors will be......\(^o\)

The electric field in an electromagnetic wave is given as \(\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} NC ^{-1}\) Where \(\omega\) and \(c\) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \(5 \times 10^{-4}\, m ^3\) will be \(.....\times 10^{-13}\,J\) (Given \(\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2\) )

Match List-I with List-II.

List-I	List-II
(A) Mass density	(I) [ML2T-3]
(B) Impulse	(II) [MLT-1]
(C) Power	(III) [ML2T0]
(D) Moment of inertia	(IV) [ML-3T0]

Choose the correct answer from the options given below :

A particle moves such that its position vector \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}\) where \(\omega\) is a constant and \(t\) is time. Then which of the following statements is true for the velocity \(\overrightarrow{\mathrm{v}}(\mathrm{t})\) and acceleration \(\overrightarrow{\mathrm{a}}(\mathrm{t})\) of the particle

In the given figure, the \(emf\) of the cell is \(2.2\, {V}\) and if internal resistance is \(0.6\, \Omega\). Calculate the power dissipated in the whole circuit: (in \(W\))

The initial velocity \(v_{i}\) required to project a body vertically upward from the surface of the earth to reach a height of \(10\, R ,\) where \(R\) is the radius of the earth, may be described in terms of escape velocity \(v_{ e }\) such that \(v_{i}=\sqrt{\frac{x}{y}} \times v_{ e } .\) The value of \(x\) will be ...... .

A heating element has a resistance of  \(100\,\Omega \) at room temperature. When it is connected to a supply of  \(220\,V,\)  a steady current of \(2\,A\)  passes in it and temperature is \(500\,^oC\) more than room temperature. What is the temperature coefficient resistance of the heating element?

The speed of a longitudinal wave in a metallic bar is \(400~m/s.\) If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to ___________ \(m / s\).