Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason R : At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below:

The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :

The approximate height from the surface of earth at which the weight of the body becomes {1 \over 3} of its weight on the surface of earth is : [Radius of earth R = 6400 km and $$\sqrt{3}$$ = 1.732]

The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3$$\rho$$ and 5$$\rho$$ respectively. The ratio of their acceleration due to gravity is :

Three identical particles $$\mathrm{A},\mathrm{B}$$ and $$\mathrm{C}$$ of mass $$100\mathrm{kg}$$ each are placed in a straight line with $$\mathrm{AB}=\mathrm{BC}=13\mathrm{m}$$. The gravitational force on a fourth particle $$\mathrm{P}$$ of the same mass is $$\mathrm{F}$$, when placed at a distance $$13\mathrm{m}$$ from the particle $$\mathrm{B}$$ on the perpendicular bisector of the line $$\mathrm{AC}$$. The value of $$\mathrm{F}$$ will be approximately :

The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = $$\pi$$2 ms$$-$$2)

An object is taken to a height above the surface of earth at a distance {5 \over 4} R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be :

The percentage decrease in the weight of a rocket, when taken to a height of $$32\mathrm{km}$$ above the surface of earth will, be : $$($$ Radius of earth $$=6400\mathrm{km})$$

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be : (Take radius of earth $$=6400\mathrm{km}$$ and $$\mathrm{g}=10{\mathrm{ms}}^{-2}$$ )

Two satellites $$\mathrm{A}$$ and $$\mathrm{B}$$, having masses in the ratio $$4:3$$, are revolving in circular orbits of radii $$3\mathrm{r}$$ and $$4\mathrm{r}$$ respectively around the earth. The ratio of total mechanical energy of $$\mathrm{A}$$ to $$\mathrm{B}$$ is :

A body of mass $$\mathrm{m}$$ is projected with velocity $$\lambda v_{\mathrm{e}}$$ in vertically upward direction from the surface of the earth into space. It is given that $$v_{\mathrm{e}}$$ is escape velocity and $$\lambda (R : radius of earth)

If the radius of earth shrinks by $$2\%$$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

An object of mass $$1\mathrm{kg}$$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $$\mathrm{g}=10{\mathrm{ms}}^{-2}$$ and radius of earth $$=6400\mathrm{km}$$ ]

Using Young's double slit experiment, a monochromatic light of wavelength 5000 $$\stackrel{o}{A}$$ produces fringes of fringe width 0.5 mm. If another monochromatic light of wavelength 6000 $$\stackrel{o}{A}$$ is used and the separation between the slits is doubled, then the new fringe width will be :

In Young's double slit experiment performed using a monochromatic light of wavelength $$\lambda$$, when a glass plate ($$\mu$$ = 1.5) of thickness x$$\lambda$$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be :

For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :

The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio {{{I_{\max }} + {I_{\min }}} \over {{I_{\max }} - {I_{\min }}}} is {5 \over x}. Then, the value of x will be equal to :

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $$\pi$$/2 at point P and $$\pi$$ at point Q. Then the difference between the resultant intensities at P and Q will be :