General
✓✗A geostationary satellite of mass 500 kg is in an orbit of radius 4.2 × 107 m. Its kinetic energy is about (GME = 4 × 1014 SI)
- 9.5 × 109 J
- 2.4 × 109 J
- 1.2 × 109 J
- 4.8 × 109 J
General
✓✗Two bodies at the earth's surface are lifted by the same height h (h << R). The increase in their gravitational potential energy is
- zero
- mgh for each, so it depends on their masses
- the same for both
- independent of h
General
✓✗The mass of the moon is about 1/81 of the earth's and its radius about 1/4. The value of g on the moon compared with that on the earth is about
- 16/81
- 4/81
- 1/81
- 1/4
General
✓✗The escape speed from a spherical planet is 4 km/s. A body projected from it at 5 km/s will have a speed far away from the planet of
- \( \sqrt{41} \) km/s
- 1 km/s
- 3 km/s
- 9 km/s
General
✓✗At what depth below the earth's surface is g half of its surface value?
- 2R/3
- R/4
- R/2
- R
General
✓✗If ve is the escape velocity and vo is the orbital velocity of a satellite in an orbit close to the earth's surface, these are related by
- \( v_o = \sqrt2\,v_e \)
- \( v_e = \sqrt{2v_o} \)
- \( v_e = \sqrt2\,v_o \)
- vo = ve
General
✓✗Gravitational potential at a point is
- the work done per unit mass in bringing a body from infinity to that point
- the potential energy of any mass
- always positive
- the force on a unit mass
General
✓✗The ratio of the gravitational forces exerted by the earth on the moon and by the moon on the earth is
- 1/81
- 1
- 81
- 6
General
✓✗The escape velocity for the earth is v. A planet having 9 times the mass of the earth and 16 times its radius has an escape velocity of
- \( \dfrac{2v}{3} \)
- \( \dfrac{3v}{4} \)
- \( \dfrac v3 \)
- \( \dfrac{9v}{4} \)
General
✓✗The centripetal force needed for a satellite to move in its orbit is provided by
- the satellite's inertia
- the rocket engine
- the gravitational pull of the earth
- air resistance
General
✓✗A particle of mass M is situated at the centre of a spherical shell of the same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 from the centre will be
- \( \dfrac{GM}{a} \)
- \( \dfrac{4GM}{a} \)
- \( \dfrac{3GM}{a} \)
- \( \dfrac{2GM}{a} \)
General
✓✗A body is taken from the surface to a depth of R/4. Its weight becomes
- 1/4 of its surface weight
- 3/4 of its surface weight
- 9/16 of its surface weight
- 1/16 of its surface weight
General
✓✗The gravitational potential V varies with distance x as V = 4x2 J/kg. The gravitational field at x = 2 m is
- 16 N/kg
- −8 N/kg
- −16 N/kg
- zero
General
✓✗The SI unit of gravitational potential is
- J kg−1
- J
- N m
- N kg−1
General
✓✗A planet's distance from the sun varies from 2 × 1011 m to 3 × 1011 m. The ratio of its maximum to minimum speed is
- 2.25
- 0.67
- 1.22
- 1.5