General
✓✗The earth's orbit has a radius of 1.5 × 1011 m and a period of 3.15 × 107 s. The mass of the sun is about (G = 6.67 × 10−11 SI)
- 2 × 1033 kg
- 2 × 1027 kg
- 2 × 1030 kg
- 6 × 1024 kg
General
✓✗If the distance between the earth and the sun were halved, the length of the year would become
- \( \dfrac{1}{2\sqrt2} \) of the present year
- one-fourth of the present year
- twice the present year
- half the present year
General
✓✗A spherical cavity of radius R/2 is made in a uniform solid sphere of mass M and radius R, with the centre of the cavity at a distance R/2 from the centre of the sphere (M is the mass before the cavity was made). The magnitude of the gravitational field at the centre of the sphere is
- \( \dfrac{GM}{8R^2} \)
- \( \dfrac{GM}{14R^2} \)
- \( \dfrac{GM}{2R^2} \)
- zero
General
✓✗Gravitational field intensity at a point is defined as
- the potential energy of a unit mass
- the gravitational force on a unit mass placed there
- the force on any mass
- the work done to bring a unit mass from infinity
General
✓✗Two identical spheres each of mass M and radius R touch each other. The gravitational force between them is
- \( \dfrac{GM^2}{2R^2} \)
- \( \dfrac{GM^2}{4R^2} \)
- \( \dfrac{GM^2}{R^2} \)
- infinite
General
✓✗Two satellites of masses m and 2m revolve around the earth in the same circular orbit. The ratio of their periods is
- \( 1 : \sqrt2 \)
- 1 : 2
- 1 : 1
- 2 : 1
General
✓✗Two satellites move in the same circular orbit around the earth. They must have the same
- mass
- angular momentum
- speed and period
- kinetic energy
General
✓✗The weight of a body on the surface of the earth is W. Its weight at the centre of the earth is
- W/2
- zero
- W
- infinite
General
✓✗The SI unit of G is
- N m kg−1
- N kg−2
- kg m s−2
- N m2 kg−2
General
✓✗Four equal masses m are placed at the corners of a square of side a. The gravitational potential energy of the system is
- \( -\dfrac{Gm^2}{a}(2 + \sqrt2) \)
- \( -\dfrac{4Gm^2}{a} \)
- \( -\dfrac{6Gm^2}{a} \)
- \( -\dfrac{Gm^2}{a}(4 + \sqrt2) \)
General
✓✗Two planets have masses in the ratio 1 : 2 and radii in the ratio 2 : 1. The ratio of the accelerations due to gravity on their surfaces is
- 8 : 1
- 1 : 4
- 1 : 8
- 2 : 1
General
✓✗The escape speed from the moon (M = 7.4 × 1022 kg, R = 1.74 × 106 m, G = 6.67 × 10−11 SI) is about
- 11.2 km/s
- 2.4 km/s
- 1.7 km/s
- 5.3 km/s
General
✓✗A particle of mass m is kept at rest at a height 3R from the surface of the earth, where R is the radius of the earth and M is the mass of the earth. The minimum speed with which it should be projected so that it does not return back is (g is the acceleration due to gravity on the surface of the earth)
- \( \left(\dfrac{GM}{2R}\right)^{1/2} \)
- \( \left(\dfrac{2g}{R}\right)^{1/2} \)
- \( \left(\dfrac{GM}{R}\right)^{1/2} \)
- \( \left(\dfrac{gR}{4}\right)^{1/2} \)
General
✓✗A satellite of mass 500 kg orbits the earth at a height of 6400 km (R = 6400 km, g = 10 m s−2). The energy needed to take it out of the earth's gravitational field is
- 1.6 × 1010 J
- 3.2 × 1010 J
- 4 × 109 J
- 8 × 109 J
General
✓✗A satellite in a circular orbit is acted upon by a small air drag. Over a long time, the drag force does negative work W on it. The increase in the satellite's kinetic energy is
- 2|W|
- |W|/2
- |W|
- zero