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Prove that `g_h=g(1-"2h"/R)` where gh is the acceleration due to gravity at altitude h and h << R (R is the radius of the earth).
Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22 × 108 m. Show that the mass of Jupiter is about one-thousandth that of the sun.
A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at lowest point as 7 m/s. Find the velocity at the highest point. [Acceleration due to gravity = 9.8 m/s2 ]
Derive an expression for critical velocity of a satellite revolving around the earth in a circular orbit.
A sonometer wire vibrates with frequency n1 in air under suitable load of specific gravity of . When the load is immersed in water, the frequency of vibration of wire n2 will be .........
A hole is drilled half way to the centre of the Earth. A body is dropped into the hole. How much will it weigh at the bottom of the hole if the weight of the body on the Earth’s surface is 350 N?
What is the decrease in weight of a body of mass 600kg when it is taken in a mine of depth 5000m?
[ Radius of earth = 6400km, g = 9.8 m/s2 ]
Calculate the density of paraffin oil, if glass capillary of diameter 0.25 mm dipped in paraffin oil of surface tension 0.0245 N/m rises to a height of 4 cm. (Angle of contact of paraffin with glass = 28° and acceleration due to gravity = 9.8 m/s2.)