A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 respectively. The time period of its oscillation is given as :

T0 is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to {1 \over {16}} times of its initial value, the modified time period is :

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is {{3E} \over 4} then its displacement 'y' is given by :

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant t = {T \over 4}s starting from mean position. Assume that the initial phase of the oscillation is zero.

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :

A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density {1 \over 4} times that of the bob and the length of the thread is increased by 1/3rd of the original length, then the time period of the simple harmonic oscillations will be :-

For a body executing S.H.M. : (1) Potential energy is always equal to its K.E. (2) Average potential and kinetic energy over any given time interval are always equal. (3) Sum of the kinetic and potential energy at any point of time is constant. (4) Average K.E. in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below :

A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

Match List - I with List - II. List I List II (a) Source of microwave frequency (i) Radioactive decay of nucleus (b) Source of infrared frequency (ii) Magnetron (c) Source of Gamma Rays (iii) Inner shell electrons (d) Source of X-rays (iv) Vibration of atoms and molecules (v) LASER (vi) RC circuit Choose the correct answer from the options given below :

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, $$\overrightarrow{B}$$ = 8.0 $$\times$$ 10$$-$$8 $$\hat{z}$$T. The value of electric field at this point is : (speed of light = 3 $$\times$$ 108 ms$$-$$1) $$\hat{x}$$, $$\hat{y}$$, $$\hat{z}$$ are unit vectors along x, y and z directions.

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (Ue) and magnetic (Um) fields is :

A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, $$\overrightarrow{B}=2.0\times 10^{-8}\hat{k}T$$. (where, $$\hat{k}$$ is unit vector along z-direction) What is $$\overrightarrow{E}$$ at this point?

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $$\left(\overrightarrow{E}\right)$$ and magnetic field $$\left(\overrightarrow{B}\right)$$ components.

In an electromagnetic wave the electric field vector and magnetic field vector are given as $$\overrightarrow{E}=E_0\hat{i}$$ and $$\overrightarrow{B}=B_0\hat{k}$$ respectively. The direction of propagation of electromagnetic wave is along :

Intensity of sunlight is observed as 0.092 Wm$$-$$2 at a point in free space. What will be the peak value of magnetic field at the point? ($${\epsilon }_0=8.85\times 10^{-12}{C}^2{N}^{-1}{m}^{-2}$$)

A linearly polarized electromagnetic wave in vacuum is $$E=3.1\cos \left[(1.8)z-(5.4\times {10}^6)t\right]\hat{i}N/C$$ is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

The relative permittivity of distilled water is 81. The velocity of light in it will be : (Given $$\mu$$r = 1)

A light beam is described by E = 800\sin \omega \left( {t - {x \over c}} \right). An electron is allowed to move normal to the propagation of light beam with a speed of 3 $$\times$$ 107 ms$$-$$1. What is the maximum magnetic force exerted on the electron?

Electric field in a plane electromagnetic wave is given by E = 50 sin(500x $$-$$ 10 $$\times$$ 1010 t) V/m The velocity of electromagnetic wave in this medium is : (Given C = speed of light in vacuum)