Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is
(a) -6Gm/r
(b) -9Gm/r
(c) Zero
(d) -4Gm/r
A geostationary satellite orbits around the earth in a circular orbit of radius 36,000km. Then, the time period of a spy satellite orbiting a few hundred km above the earth’s surface (R =6,400km) will approximately be
(a) (l/2)hr
(b) 1 hr
(c) 2 hr
(d) 4 hr
A simple pendulum has a time period T1 when on the earth’s surface, and T2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T2/T1 is
(a) 1
(b) 3
(c) 4
(d) 2
An artificial satellite moving in a circular orbit around the earth has a total (K.E. + P.E.) energy E0. Its potential energy is
(a) – E0
(b) 1.5 E0
(c) 2 E0
(d) E0
The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’ and ‘R’ (radius of the earth) is 10 m/s2 and 6400 km respectively. The required energy for this work will be
(a) 6.4 x 1010 Joules
(b) 6.4 x 1011 Joules
(c) 6.4 x 108 Joules
(d) 6.4 x 109 Joules