Two particles move at right angle to each other. Their de-Broglie wavelengths are $${\lambda }_1$$ and $${\lambda }_2$$ respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength $${\lambda }_2$$ of the final particle, is given by :

In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths {{{\lambda _A}} \over {{\lambda _B}}} is close to :

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to: ({{{hc} \over e}} = 1240 nm eV)

When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the current is –V0/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is – V0. The threshold frequency for photoelectric emission is :

A metal plate of area 1 $$\times$$ 10–4 m2 is illuminated by a radiation of intensity 16 mW/m2. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photoelectrons per second and their maximum energy, respectively, will be

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10–12 m, the minimum electron energy required is close to -

Surface of certain metal is first illuminated with light of wavelength $$\lambda$$1 = 350 nm and then, by light of wavelength $$\lambda$$2 = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to : (Energy of photon n = {{1240} \over {\lambda (in\,mm)}}eV)

The magnetic field associated with a light wave is given, at the origin, by B = B0 [sin(3.14 $$\times$$ 107)ct + sin(6.28 $$\times$$ 107)ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons ? (Take c = 3 $$\times$$ 108 ms$$-$$1, h = 6.6 $$\times$$ 10$$-$$34J-s)

A paramagnetic material has 1028 atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 $$\times$$ 10–4. Its susceptibility at 300 K is :

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45o, and 40 times per minute where the dip is 30o. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio {{{B_1}} \over {{B_2}}} is best given by :

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing, through their midpoint P, at angle q = 45° with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant ? (d is much larger than the dimensions of the dipole)

At some location on earth, the horizontal component of earth’s magnetic field is 18 × 10–6 T. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45o angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is -

A magnet of total magnetic moment 10-2 $$\hat{i}$$ A-m2 is placed in a time varying magnetic field, B$$\hat{i}$$ (cos $$\omega t$$) where B = 1 Tesla and $$\omega$$ = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is -

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The corecivity of the bar magnet is :

A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 $$\times$$ 10–6 J/ T when a magnetic intensity of 60 $$\times$$ 103 A/m is applied. Its magnetic susceptibility is

Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA/TB, is ;

The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the planet is {1 \over 9} th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given ; Mass of planet = 8 × 1022 kg, Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10–11 Nm2 /kg2]

The value of acceleration due to gravity at Earth's surface is 9.8 ms–2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms–2, is close to : (Radius of earth = 6.4 × 106 m)