At a certain place the angle of dip is 30$${}^{\circ }$$ and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that certain place, is :

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 $$\times$$ 10$$-$$5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is : [Permeability of free space $$\mu$$0 = 4$$\pi$$ $$\times$$ 10$$-$$7 Wb/A-m]

A bar magnet having a magnetic moment of 2.0 $$\times$$ 105 JT$$-$$1, is placed along the direction of uniform magnetic field of magnitude B = 14 $$\times$$ 10$$-$$5 T. The work done in rotating the magnet slowly through 60$${}^{\circ }$$ from the direction of field is :

Given below are two statements : Statement I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the correct answer from the options given below :

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has

An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of 1 $$\times$$ 10$$-$$4 Wbm$$-$$2. The frequency of revolution of the electron will be : (Take mass of electron = 9.0 $$\times$$ 10$$-$$31 kg)

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $$3\mathrm{s}$$ and $$4\mathrm{s}$$ respectively. If their moments of inertia are in the ratio of $$3:2$$, then the ratio of their magnetic moments will be:

A magnet hung at $$45^{\circ }$$ with magnetic meridian makes an angle of $$60^{\circ }$$ with the horizontal. The actual value of the angle of dip is -

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place $$\mathrm{P}$$ of $$\mathrm{dip}30^{\circ }$$. The number of oscillations per minute become 10 at another place $$\mathrm{Q}$$ of $$60^{\circ }$$ dip. The ratio of the total magnetic field at the two places $$\left(B_Q:B_P\right)$$ is :

The vertical component of the earth's magnetic field is $$6\times 10^{-5}\mathrm{T}$$ at any place where the angle of dip is $$37^{\circ }$$. The earth's resultant magnetic field at that place will be $$($$Given $$\tan 37^{\circ }=\frac{3}{4})$$

The escape velocity of a body on a planet 'A' is 12 kms$$-$$1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :

The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be

Water falls from a 40 m high dam at the rate of 9 $$\times$$ 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is : (Take g = 10 ms$$-$$2)

Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be :

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?

The distance of the Sun from earth is 1.5 $$\times$$ 1011 m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

Four spheres each of mass m from a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is :

Given below are two statements : Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below.

The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by : (Given R = radius of earth)