For particle P revolving round the centre O with radius of circular path $$\mathrm{r}$$ and angular velocity $$\omega$$, as shown in below figure, the projection of OP on the $$x$$-axis at time $$t$$ is

A mass $$m$$ is attached to two strings as shown in figure. The spring constants of two springs are $${\mathrm{K}}_1$$ and $${\mathrm{K}}_2$$. For the frictionless surface, the time period of oscillation of mass $$m$$ is :

The ratio of average electric energy density and total average energy density of electromagnetic wave is :

Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} LIST I LIST II A. Microwaves I. Physiotherapy B. UV rays II. Treatment of cancer C. Infra-red light III. Lasik eye surgery D. X-ray IV. Aircraft navigation Choose the correct answer from the options given below:

Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-amwm{font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0lax{text-align:left;vertical-align:top} List I List II A. Microwaves I. Radio active decay of the nucleus B. Gamma rays II. Rapid acceleration and deceleration of electron in aerials C. Radio waves III. Inner shell electrons D. X-rays IV. Klystron valve Choose the correct answer from the options given below :

A point source of $100\mathrm{W}$ emits light with $5 \%$ efficiency. At a distance of $5\mathrm{m}$ from the source, the intensity produced by the electric field component is:

Given below are two statements : Statement I : Electromagnetic waves are not deflected by electric and magnetic field. Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as {E_0} = \sqrt {{{{\mu _0}} \over {{\varepsilon _0}}}} {B_0}. In the light of the above statements, choose the correct answer from the options given below :

Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of light in a medium is independent of the wavelength of light. C. The speed of light is independent of the motion of the source. D. The speed of light in a medium is independent of intensity. Choose the correct answer from the options given below:

Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I List II A. Gauss's Law in Electrostatics I. \oint {\overrightarrow E \,.\,d\overrightarrow l = - {{d{\phi _B}} \over {dt}}} B. Faraday's Law II. $$\oint \overrightarrow{B}.d\overrightarrow{A}=0$$ C. Gauss's Law in Magnetism III. \oint {\overrightarrow B \,.\,d\overrightarrow l = {\mu _0}{i_c} + {\mu _0}{ \in _0}{{d{\phi _E}} \over {dt}}} D. Ampere-Maxwell Law IV. \oint {\overrightarrow E \,.\,d\overrightarrow s = {q \over {{ \in _0}}}} Choose the correct answer from the options given below :

An electromagnetic wave is transporting energy in the negative $$z$$ direction. At a certain point and certain time the direction of electric field of the wave is along positive $$y$$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by $${\mathrm{E}}_{\mathrm{x}}={\mathrm{E}}_{\mathrm{o}}\sin (\mathrm{kz}-\omega \mathrm{t})$$ $${\mathrm{B}}_{\mathrm{y}}={\mathrm{B}}_{\mathrm{o}}\sin (\mathrm{kz}-\omega \mathrm{t})$$ Then the correct relation between E$${}_0$$ and B$${}_0$$ is given by

In $$\overrightarrow{E}$$ and $$\overrightarrow{K}$$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : ($$\omega$$ - angular frequency) :

Match List I with List II of Electromagnetic waves with corresponding wavelength range : .tg {border-collapse:collapse;border-spacing:0;width:100%} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I List II (A) Microwave (I) $400\mathrm{nm}$ to $1\mathrm{nm}$ (B) Ultraviolet (II) $1\mathrm{nm}$ to $10^{-3}\mathrm{nm}$ (C) X-Ray (III) $1\mathrm{mm}$ to $700\mathrm{nm}$ (D) Infra-red (IV) $0.1\mathrm{m}$ to $1\mathrm{mm}$ Choose the correct answer from the options given below:

In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative $$z$$-axis and magnetic field is along the positive $$x$$-axis. Then the direction of propagation of electromagnetic wave is:

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$ Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason R : Infrared EM waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below.

A plane electromagnetic wave of frequency $$20\mathrm{MHz}$$ propagates in free space along $$\mathrm{x}$$-direction. At a particular space and time, $$\overrightarrow{\mathrm{E}}=6.6\hat{j}\mathrm{V}/\mathrm{m}$$. What is $$\overrightarrow{\mathrm{B}}$$ at this point?

The electric field in an electromagnetic wave is given as $$\overrightarrow{\mathrm{E}}=20\sin \omega \left(\mathrm{t}-\frac{x}{\mathrm{c}}\right)\overrightarrow{\mathrm{j}}{\mathrm{NC}}^{-1}$$ where $$\omega$$ and $$c$$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $$5\times 10^{-4}{\mathrm{m}}^3$$ will be (Given $${\epsilon }_0=8.85\times 10^{-12}{\mathrm{C}}^2/{\mathrm{Nm}}^2$$ )

The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is $$6.0\times 10^{-7}\mathrm{T}$$. The maximum value of electric field in the electromagnetic wave is

The energy of an electromagnetic wave contained in a small volume oscillates with