A plane electromagnetic wave of frequency 20 MHz travels in free space along the $+x$ direction. At a particular point in space and time, the electric field vector of the wave is ${\mathrm{E}}_y=9.3{\mathrm{Vm}}^{-1}$. Then, the magnetic field vector of the wave at that point is

Arrange the following in the ascending order of wavelength $(\lambda )$ : (A) Microwaves $\left({\lambda }_1\right)$ (B) Ultraviolet rays $\left({\lambda }_2\right)$ (C) Infrared rays $\left({\lambda }_3\right)$ (D) X-rays $\left({\lambda }_4\right)$ Choose the most appropriate answer from the options given below :

Due to presence of an em-wave whose electric component is given by $E=100\sin (\omega t-kx){\mathrm{NC}}^{-1}$ a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

The unit of $\sqrt{\frac{2I}{{\epsilon }_{0}c}}$ is :(I = intensity of an electromagnetic wave, c = speed of light)

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., $\frac{dm}{dt}\propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

A force $\overrightarrow{\mathrm{F}}=2\hat{i}+\mathrm{b}\hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2\hat{j}-\hat{k}$ What will be the value of $b$, if work done on the particle is zero.

A body of mass 4 kg is placed on a plane at a point $P$ having coordinate $(3,4)\mathrm{m}$. Under the action of force $\overrightarrow{\mathrm{F}}=(2\hat{i}+3\hat{j})\mathrm{N}$, it moves to a new point Q having coordinates $(6,10)\mathrm{m}$ in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :

A ball having kinetic energy KE, is projected at an angle of $60^{\circ }$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

A force $\mathrm{F}=\alpha +\beta {\mathrm{x}}^2$ acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant $\alpha =1\mathrm{N}$ then $\beta$ will be

A bead of mass ' $m$ ' slides without friction on the wall of a vertical circular hoop of radius ' $R$ ' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ' $R$ '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' $R$ ', would be (spring constant is ' $k$ ', $g$ is accleration due to gravity)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$ Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below

An object of mass 1000 g experiences a time dependent force $\vec{F}=\left(2t\hat{i}+3t^2\hat{j}\right)N$. The power generated by the force at time $t$ is:

Which one of the following forces cannot be expressed in terms of potential energy?

A particle is released from height $S$ above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle $45^{\circ }$ with the horizontal. The friction coefficient between the block and the surface is 0.25 . The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is :

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_0$. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

An alternating current is given by $\mathrm{I}={\mathrm{I}}_{\mathrm{A}}\sin \omega \mathrm{t}+{\mathrm{I}}_{\mathrm{B}}\cos \omega \mathrm{t}$. The r.m.s current will be

An ac current is represented as $$i=5\sqrt{2}+10\cos \left(650\pi t+\frac{\pi }{6}\right)Amp$$ The r.m.s value of the current is

An alternating current is represented by the equation, $i=100\sqrt{2}\sin (100\pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

An electric bulb rated as $100\mathrm{W}-220\mathrm{V}$ is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is :