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
If the distance between the earth and the sun were half its present value, the number of days in a year would have been
(a) 64.5
(b) 129
(c) 182.5
(d) 730
A pulley of radius 2 m is rotated about its axis by a force F =20t-5t2 newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kgm2, the number of rotations made by the pulley before its direction of motion it reversed, is
(a) more than 6 but less than 9
(b) more than 9
(c) less than 3
(d) more than 3 but less than 6
From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc is
(a) (40/9)MR2
(b) 10MR2
(c) (37/9)MR2
(d) 4MR2
A bob of mass m attached to an inextensible string of length is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension
(a) Angular momentum changes in direction but not in magnitude
(b) Angular momentum changes both in direction and magnitude
(c) Angular momentum is conserved
(d) Angular momentum changes in magnitude but not in direction.
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