A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass $${m \over {10}}$$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :

A beam of electromagnetic radiation of intensity 6.4 × 10^–5 W/cm² is comprised of wavelength, $$\lambda $$ = 310 nm. It falls normally on a metal (work function $$\phi $$ = 2eV) of surface area of 1 cm². If one in 10³ photons ejects an elctron, total number of electrons ejected in 1 s is 10^x. (hc = 1240 eVnm, 1eV = 1.6 × 10^–19 J), then x is _____.

Visible light of wavelength 6000 $$ \times $$ 10^-8 cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60^o from the central maximum. If the first minimum is produced at $$\theta $$₁, then $$\theta $$₁, is close to :

If the magnetic field in a plane electromagnetic wave is given by
$$\overrightarrow B $$ = 3 $$ \times $$ 10^-8 sin(1.6 $$ \times $$ 10³x + 48 $$ \times $$ 10¹⁰t)$$\widehat j$$ T, then what will be expression for electric field ?

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), the kinetic energy of the particle (in )) is :
(Figure drawn is schematic and not to scale; take g = 10 ms^-2)

The current I₁ (in A) flowing through 1 $$\Omega $$ resistor in the following circuit is :

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece, should be close to :

Which of the following gives a reversible operation?

As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be:

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $$\gamma $$ = 1.40, the work done by air is : (3^1.4 = 4.6555) [Take air to be an ideal gas]

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $$ \times $$ 10^-16 s. The frequency of revolution of the electron in its first excited state (in s^-1) is :

Two moles of an ideal gas with $${{{C_P}} \over {{C_V}}} = {5 \over 3}$$ are mixed with 3 moles of another ideal gas with $${{{C_P}} \over {{C_V}}} = {4 \over 3}$$. The value of $${{{C_P}} \over {{C_V}}}$$ for the mixture is :

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm²) is 90 ms^-1. If the Young's modulus of wire is 16 $$ \times $$ 10¹¹ Nm^-2, the extension of wire over its natural length is :

Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30^o. The electric field in the region shown between them is given by :

A long solenoid of radius R carries a time (t) - dependent current
I(t)=I₀t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 $$ \le $$ t $$ \le $$ 1, the induced current (I_R) and the induced EMF(V_R) in the ring change as :

The radius of gyration of a uniform rod of length $$l$$, about an axis passing through a point $${l \over 4}$$ away from the centre of the rod, and perpendicular to it, is :

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just 10% of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is :

Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $$\phi $$_i. The magnetic flux through the area of the circular coil area is given by $$\phi $$₀. Which of the following option is correct?

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to :
(1 HP = 746 W, g = 10 ms^-2)

A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D (0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is $$\overrightarrow B = \left( {3\widehat i + 4\widehat k} \right)T$$ . The quantity of flux through the loop ABCDEFA (in Wb) is _______.

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + $$\alpha $$x) where 'x' is the distance measured from one of the plates. If (ad) << 1, the total capacitance of the system is best given by the expression :

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point:

A non-isotropic solid metal cube has coefficients of linear expansion as :
5 $$ \times $$ 10^-5/^oC along the x-axis and 5 $$ \times $$ 10^-6/^oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C $$ \times $$ 10^-6/^oC then the value of C is