Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of $$\mathrm{A}$$ is $$3v$$, the speed of $$\mathrm{B}$$ will be :

Two planets $$A$$ and $$B$$ having masses $$m_1$$ and $$m_2$$ move around the sun in circular orbits of $$r_1$$ and $$r_2$$ radii respectively. If angular momentum of $$A$$ is $$L$$ and that of $$B$$ is $$3\mathrm{L}$$, the ratio of time period $$\left(\frac{T_A}{T_B}\right)$$ is:

If $$\mathrm{G}$$ be the gravitational constant and $$\mathrm{u}$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{\mathrm{uG}}$$ :

Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} LIST I LIST II A. Kinetic energy of planet I. $$-\mathrm{GMm}/\mathrm{a}$$ B. Gravitation Potential energy of sun-planet system II. $$\mathrm{GMm}/2\mathrm{a}$$ C. Total mechanical energy of planet III. $$\frac{\mathrm{Gm}}{\mathrm{r}}$$ D. Escape energy at the surface of planet for unit mass object IV. $$-\mathrm{GMm}/2\mathrm{a}$$ (Where $$\mathrm{a}=$$ radius of planet orbit, $$\mathrm{r}=$$ radius of planet, $$\mathrm{M}=$$ mass of Sun, $$\mathrm{m}=$$ mass of planet) Choose the correct answer from the options given below :

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given $$=$$ Radius of geo-stationary orbit for earth is $$4.2\times 10^4\mathrm{km}$$)

Assuming the earth to be a sphere of uniform mass density, a body weighed $$300\mathrm{N}$$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $$R_E,g=$$ acceleration due to gravity on the surface of earth):

A microwave of wavelength $2.0\mathrm{cm}$ falls normally on a slit of width $4.0\mathrm{cm}$. The angular spread of the central maxima of the diffraction pattern obtained on a screen $1.5\mathrm{m}$ away from the slit, will be :

A monochromatic light of wavelength $6000\mathring{A}$ is incident on the single slit of width $0.01\mathrm{mm}$. If the diffraction pattern is formed at the focus of the convex lens of focal length $20\mathrm{cm}$, the linear width of the central maximum is :

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

When unpolarized light is incident at an angle of $$60^{\circ }$$ on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction in the medium is:

In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is $$7\lambda /4$$. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is :

A beam of unpolarised light of intensity $$I_0$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $$45^{\circ }$$ relative to that of $$A$$. The intensity of emergent light is:

The diffraction pattern of a light of wavelength $$400\mathrm{nm}$$ diffracting from a slit of width $$0.2\mathrm{mm}$$ is focused on the focal plane of a convex lens of focal length $$100\mathrm{cm}$$. The width of the $$1^{\text{st }}$$ secondary maxima will be :

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:

Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is :

Given below are two statements : Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements, chose the correct answer from the options given below :

A galvanometer $(G)$ of $2\Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is :

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2\mathrm{V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $$\frac{A}{3}$$ and the height is $$d$$, the capacitance of the arrangement is :