A space ship of mass $$2\times 10^4\mathrm{kg}$$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $$g=10\mathrm{m}/{\mathrm{s}}^2$$ and radius of earth $$=6400\mathrm{km}$$ ):

If $$\mathrm{V}$$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $$\rho$$ and $$\rho /3$$ respectively. The ratio of acceleration due to gravity at their surfaces $$\left(g_A:g_B\right)$$ will be:

The time period of a satellite, revolving above earth's surface at a height equal to $$\mathrm{R}$$ will be (Given $$g={\pi }^2\mathrm{m}/{\mathrm{s}}^2,\mathrm{R}=$$ radius of earth)

Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below

Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $$d=\frac{R}{2}$$ from the surface of earth, if its weight on the surface of earth is 200 N, will be: (Given R = radius of earth)

The acceleration due to gravity at height $$h$$ above the earth if $$h

The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be -

Given below are two statements: Statement I: If $$\mathrm{E}$$ be the total energy of a satellite moving around the earth, then its potential energy will be $$\frac{E}{2}$$. Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $$\mathrm{E}$$. In the light of the above statements, choose the most appropriate answer from the options given below

The weight of a body on the earth is $$400\mathrm{N}$$. Then weight of the body when taken to a depth half of the radius of the earth will be:

Given below are two statements : one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$. Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere. Reason R : The escape velocity on moon is very small as compared to that on earth. In the light of the above statements, choose the correct answer from the options given below:

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $$\mathrm{W}$$ on earth will weigh on that planet:

The weight of a body on the surface of the earth is $$100\mathrm{N}$$. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

Choose the incorrect statement from the following:

'$$n$$' polarizing sheets are arranged such that each makes an angle $$45^{\circ }$$ with the preceeding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be $$I/64$$. The value of $$n$$ will be:

Two polaroide $$\mathrm{A}$$ and $$\mathrm{B}$$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $$\mathrm{C}$$ is placed between $$\mathrm{A}$$ and $$\mathrm{B}$$ bisecting angle between them. If intensity of unpolarized light is $${\mathrm{I}}_0$$ then intensity of transmitted light after passing through polaroid $$\mathrm{B}$$ will be:

In a Young's double slit experiment, two slits are illuminated with a light of wavelength $$800\mathrm{nm}$$. The line joining $$A_{1}P$$ is perpendicular to $$A_1{A}_2$$ as shown in the figure. If the first minimum is detected at $$P$$, the value of slits separation 'a' will be: The distance of screen from slits D = 5 cm

In Young's double slits experiment, the position of 5$${}^{\mathrm{th}}$$ bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation between the slits is :

Given below are two statements : Statement I : If the Brewster's angle for the light propagating from air to glass is $${\theta }_{\mathrm{B}}$$, then the Brewster's angle for the light propagating from glass to air is $$\frac{\pi }{2}-{\theta }_B$$ Statement II : The Brewster's angle for the light propagating from glass to air is $${\tan }^{-1}({\mu }_{\mathrm{g}})$$ where $${\mu }_{\mathrm{g}}$$ is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below :