General
✓✗The orbital speed of an earth satellite is 7.9 km/s close to the surface. At an orbit radius of 4R, its speed is about
- 7.9 km/s
- 15.8 km/s
- 1.98 km/s
- 3.95 km/s
General
✓✗The distances of two planets from the sun are 1013 m and 1012 m respectively. The ratio of the time periods of the planets is
- \( 1/\sqrt{10} \)
- 10
- \( 10\sqrt{10} \)
- \( \sqrt{10} \)
General
✓✗If the distance of a planet from the sun is doubled, its period of revolution becomes
- \( 2\sqrt2 \) times
- 2 times
- 4 times
- \( \sqrt2 \) times
General
✓✗A body is to be thrown from the earth so that it reaches infinity with a speed of 11.2 km/s. Its speed of projection must be
- 22.4 km/s
- \( 11.2\sqrt2 \) km/s
- 11.2 km/s
- 15 km/s
General
✓✗The gravitational potential at a distance r (r > R) from the centre of the earth is V. The magnitude of the gravitational field there is
- \( \dfrac{|V|}{r^2} \)
- \( \dfrac{|V|}{r} \)
- zero
- |V|r
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
✓✗A comet moves in a highly elliptical orbit around the sun. Which quantity is constant throughout its motion?
- Its speed
- Its angular momentum about the sun
- Its kinetic energy
- Its potential energy
General
✓✗If the radius of the earth decreased by 1 % with its mass unchanged, the value of g on its surface would
- decrease by about 2 %
- increase by about 1 %
- remain unchanged
- increase by about 2 %
General
✓✗The gravitational force between two objects is F at a separation r. At separation r/2, the force is
- F/4
- 4F
- F/2
- 2F
General
✓✗A body is dropped from a satellite moving in a circular orbit 1000 km above the earth. Relative to the earth, the body will
- spiral slowly down to the earth
- continue in the same orbit along with the satellite
- fall straight to the earth
- escape into space
General
✓✗If the earth were a uniform sphere, g at a point midway between the surface and the centre would be
- g/4
- g
- 2g
- g/2
General
✓✗The escape velocity of a body (such as a sphere of mass m) from the earth is given by (G = universal gravitational constant; Me = mass of the earth; Re = radius of the earth)
- \( \sqrt{\dfrac{2GM_em}{R_e}} \)
- \( \sqrt{\dfrac{GM_e}{R_e}} \)
- \( \sqrt{\dfrac{2GM_e}{R_e}} \)
- \( \sqrt{\dfrac{2GM_e + R_e}{R_e}} \)
General
✓✗Assertion: The escape speed from the earth is independent of the direction of projection.
Reason: The gravitational field of the earth is conservative.
Reason: The gravitational field of the earth is conservative.
- Both Assertion and Reason are true and Reason is the correct explanation of Assertion
- Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
- Assertion is true but Reason is false
- Both Assertion and Reason are false
General
✓✗The work done in moving a body of mass m from the centre of a uniform thin shell (mass M, radius R) to its surface is
- \( \dfrac{GMm}{R} \)
- \( \dfrac{GMm}{2R} \)
- zero
- \( -\dfrac{GMm}{R} \)
General
✓✗Four equal masses m are placed at the corners of a square of side a. The net gravitational force on a mass m placed at the centre is
- \( \dfrac{\sqrt2Gm^2}{a^2} \)
- zero
- \( \dfrac{2Gm^2}{a^2} \)
- \( \dfrac{4Gm^2}{a^2} \)