A monochromatic light is incident on a metallic plate having work function $\varphi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point $B$. The distance between $A$ and $B$ is : (Given : The magnitude of charge of an electron is e and mass is $\mathrm{m},\mathrm{h}$ is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

An electron with mass ' m ' with an initial velocity $(\mathrm{t}=0)\overrightarrow{\mathrm{v}}={\mathrm{v}}_0\hat{i}\left({\mathrm{v}}_0>0\right)$ enters a magnetic field $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\hat{j}$. If the initial de-Broglie wavelength at $\mathrm{t}=0$ is ${\lambda }_0$ then its value after time ' t ' would be :

A photoemissive substance is illuminated with a radiation of wavelength ${\lambda }_i$ so that it releases electrons with de-Broglie wavelength ${\lambda }_e$. The longest wavelength of radiation that can emit photoelectron is ${\lambda }_o$. Expression for de-Broglie wavelength is given by: (m: mass of the electron, h: Planck's constant and c: speed of light)

The work function of a metal is 3 eV . The color of the visible light that is required to cause emission of photoelectrons is

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is

A small mirror of mass $m$ is suspended by a massless thread of length $l$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror ($\mathrm{c}=$ speed of light in vacuum and $g=$ acceleration 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 photoelectric effect, on increasing the intensity of incident light the stopping potential increases. Reason R : Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency. In the light of the above statements, choose the correct answer from the options given below

Match List - I with List - II. List - I List - II (A) Magnetic induction (I) Ampere meter2 (B) Magnetic intensity (II) Weber (C) Magnetic flux (III) Gauss (D) Magnetic moment (IV) Ampere meter Choose the correct answer from the options given below:

A bar magnet has total length $2 l=20$ units and the field point P is at a distance $\mathrm{d}=10$ units from the centre of the magnet. If the relative uncertainty of length measurement is $1 \%$, then uncertainty of the magnetic field at point P is :

The relationship between the magnetic susceptibility $(x)$ and the magnetic permeability $(\mu )$ is given by : ( ${\mu }_0$ is the permeability of free space and ${\mu }_T$ is relative permeability)

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility ${\chi }_{\mathrm{Mg}}=1.2\times 10^{-5}$ ) is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Magnetic monopoles do not exist.Reason (R): Magnetic field lines are continuous and form closed loops.In the light of the above statements, choose the most appropriate answer from the options given below:

A magnetic dipole experiences a torque of $80\sqrt{3}\mathrm{N}\mathrm{m}$ when placed in uniform magnetic field in such a way that dipole moment makes angle of $60^{\circ }$ with magnetic field. The potential energy of the dipole is :

A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O$ ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is ${\mathrm{F}}_1$. A spherical part of radius $\mathrm{R}/3$ is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of $M$ is found to be $F_2$. The value of ratio $F_1:F_2$ is

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $=27$ days and gravitational attraction between the satellite and the moon is neglected.

A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.Reason (R): For a central force field the angular momentum is a constant.In the light of the above statements, choose the most appropriate answer from the options given below:

$$\text{ Match the LIST-I with LIST-II }$$ .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} List - I List - II A. $$\text{ Gravitational constant }$$ I. $$\left[{\mathrm{LT}}^{-2}\right]$$ B. $$\text{ Gravitational potential energy }$$ II. $$\left[{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$$ C. $$\text{ Gravitational potential }$$ III. $$\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$$ D. $$\text{ Acceleration due to gravity }$$ IV. $$\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]$$ Choose the correct answer from the options given below:

An object is kept at rest at a distance of $3 R$ above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational constant)