General
✓✗An infinite number of bodies, each of mass 2 kg, are situated on the x-axis at distances 1 m, 2 m, 4 m, 8 m, ... from the origin. The resulting gravitational potential due to this system at the origin will be
- −4G
- \( -\dfrac83G \)
- −G
- \( -\dfrac43G \)
General
✓✗A body is weighed with a spring balance at the poles and at the equator. The reading is
- slightly larger at the equator
- zero at the equator
- the same at both places
- slightly larger at the poles
General
✓✗The gravitational potential energy of two particles at separation r is U (a negative quantity). If their separation is slowly doubled, the work done by the gravitational force is
- U
- \( \dfrac U2 \)
- \( -\dfrac U2 \)
- 2U
General
✓✗Two satellites of the earth, S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?
- The time period of S1 is four times that of S2.
- The kinetic energies of the two satellites are equal.
- S1 and S2 are moving with the same speed.
- The potential energies of the earth and satellite in the two cases are equal.
General
✓✗The value of the universal gravitational constant G is about
- 6.67 × 10−11 N m2 kg−2
- 6.67 × 1011 N m2 kg−2
- 6.67 × 10−11 N kg−1
- 9.8 N m2 kg−2
General
✓✗The escape speed from a planet is ve. A body is projected from its surface with speed 1.5ve. Its speed at a very large distance is
- \( \dfrac{\sqrt5}{2}v_e \)
- \( \dfrac{3}{2}v_e \)
- ve
- \( \dfrac12v_e \)
General
✓✗A satellite revolves close to the earth's surface. If gravity suddenly vanished, the satellite would
- fall to the earth
- move radially outward
- stop in space
- move along the tangent to its orbit with its orbital speed
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
✓✗A body weighs 120 N on the earth. Its weight on a planet with twice the earth's mass and twice its radius is
- 240 N
- 120 N
- 60 N
- 30 N
General
✓✗The binding energy of a satellite of mass m in an orbit of radius r around the earth is
- \( \dfrac{GMm}{r} \)
- \( \dfrac{2GMm}{r} \)
- \( \dfrac{GMm}{2r} \)
- \( -\dfrac{GMm}{r} \)
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
✓✗Kepler's third law states that the square of the period of revolution (T) of a planet around the sun is proportional to the third power of the average distance r between the sun and the planet, i.e. T2 = Kr3, where K is a constant. If the masses of the sun and the planet are M and m respectively, then as per Newton's law of gravitation the force of attraction between them is \( F = \dfrac{GMm}{r^2} \). The relation between G and K is
- GK = 4π2
- \( K = \dfrac1G \)
- GMK = 4π2
- K = G
General
✓✗The mass of a planet is 4 times and its radius 2 times that of the earth. The escape speed from the planet is
- \( 11.2\sqrt2 \) km/s
- 11.2 km/s
- 22.4 km/s
- 5.6 km/s
General
✓✗At what height from the surface of the earth are the gravitational potential and the value of g equal to −5.4 × 107 J kg−1 and 6.0 m s−2 respectively? Take the radius of the earth as 6400 km.
- 2000 km
- 2600 km
- 1400 km
- 1600 km
General
✓✗The gravitational force on a body of mass m at a distance r (r < R) from the centre of a uniform solid sphere of mass M and radius R is
- \( \dfrac{GMm}{R^2} \)
- zero
- \( \dfrac{GMmr}{R^3} \)
- \( \dfrac{GMm}{r^2} \)