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08%20%20-%20%20Gravitation

08%20%20-%20%20Gravitation - 8 GRAVITATION P age 1 1 The...

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8 - GRAVITATION Page 1 1 ) The escape velocity for a body at earth’s surface is 11.2 km / s. If mass of Jupiter is 318 times that of Earth and its radius is 11.2 times that of Earth, then find the escape velocity of the same object on Jupiter. [ March, 2003 ] ( Ans: 59.7 km / s , Note: the phrase ‘ the same object ’ is unnecessary ) 2 ) A satellite weighing 2000 kg is orbiting the earth at 1600 km height above the surface. Find ( i ) the binding energy of the satellite and ( ii ) its escape velocity. Mass of earth = 6 · 10 24 kg and its radius = 6400 km. [ April, 2002 ] ( Ans: 5.0 · 10 10 J, 7.07 km / s, Note: This escape velocity is in addition to its orbital velocity and is in a direction perpendicular to it . ) 3 ) If the earth were entirely made of iron with a uniform density 7.86 · 10 3 kg / m 3 , what would be the value of acceleration due to gravity on its surface ? Radius of the earth = 6.37 · 10 6 metre ( Take G = 6.67 · 10 - 11 Nm 2 / kg 2 ). [ March, 2002 ] ( Ans: 13.98 m / s 2 ) 4 ) Find the value of ‘G’ so that the inertial mass ( m i ) and gravitational mass ( m g ) become equal on the surface of the earth. ( Mass of earth = 5.98 · 10 24 kg. Gravitational acceleration = 9.8 m / s 2 . earth’s radius = 6,400 km. ) [ October, 1997 ] ( Ans: 6.71 Nm 2 / kg 2 ) 5 ) A stone is projected with a velocity of 19.6 m / s and at 30 to the horizontal. Calculate ( i ) range, ( ii ) total time of motion and ( iii ) maximum height. [ March, 1997 ] ( Ans: ( i ) 33.95 m, ( ii ) 2 s, ( iii ) 4.9 m ) 6 ) Calculate the rate of change in gravitational acceleration ( g ) w. r. t. height from the surface of the earth. ( Radius of earth = 6400 km and g at the surface of earth = 980 cm / s 2 ) ( Ans: - 3.06 · 10 - 6 / s 2 near the surface of earth ) [ October, 1996 ] 7 ) If G = 6.67 · 10 - 11 MKS unit and radius of the earth is 6370 km, the find average density of the earth. [ March, 1996 ] ( Ans: 5.5 · 10 3 kg / m 3 ) 8 ) A sphere of mass 40 kg is
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