Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :

Take the mean distance of the moon and the sun from the earth to be $$0.4\times 10^6$$ km and $$150\times 10^6$$ km respectively. Their masses are $$8\times 10^{22}$$ kg and $$2\times 10^{30}$$ kg respectively. The radius of the earth is $$6400$$ km. Let $$\Delta F_1$$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $$\Delta F_2$$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to {{\Delta {F_1}} \over {\Delta {F_2}}} is :

A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius {R \over 2}, and the other mass, in a circular orbit of radius {3R \over 2}. The difference between the final and initial total energies is :

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then :

A plane polarized light is incident on a polariser with its pass axis aking angle $$\theta$$ with x-axis, as shown in the figure. At four different values of $$\theta ,\theta$$ = 8o, 38o, 188o and 218o, the observed intensities are same. What is the angle between the direction of polarization and x-axis ?

Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The angle between the polarizers A and C is $$\theta$$. Then :

Light of wavelength $$550$$ $$nm$$ falls normally on a slit of width $$22.0\times 10^{-5}$$ $$cm.$$ The angular position of the second minima from the central maximum will (in radians) :

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is :

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 $$\mu$$m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

A capacitor C1 = 1.0 $$\mu$$F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors $$C_2=3.0\mu F$$ and C3 = 6.0 $$\mu$$F through switch (2), as shown in the figure. The sum of final charges on C2 and C3 is :

In the following circuit, the switch S is closed at t = 0. The charge on the capacitor C1 as a function of time will be given by \left( {{C_{eq}} = {{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right)

A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is $$25\times 10^{-6}N,$$ the value of V is approximately : \left( {{ \in _o} = 8.85 \times {{10}^{ - 12}}{{{C^2}} \over {N.{m^2}}}} \right)

The equivalent capacitance between $$A$$ and $$B$$ in the circuit given below, is :

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :

A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $$340m{s}^{-1}$$)

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $$\times$$ 103 kg/m3 and its Young’s modulus is 9.27 $$\times$$ 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :

Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B s slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is 425 Hz, the original frequency of B is :

5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $$B_2$$. The ratio {{{B_1}} \over {{B_2}}} is: