General
✓✗A body is projected vertically upward from the surface of a planet of radius R with speed v and reaches a height R. The escape speed from the planet is
- 2v
- \( \sqrt2\,v \)
- v
- \( \dfrac{v}{\sqrt2} \)
General
✓✗The time period of a simple pendulum on a planet where g is one-fourth that on the earth becomes
- twice
- half
- unchanged
- four times
General
✓✗In the solar system, planets farther from the sun have
- longer periods and smaller orbital speeds
- shorter periods
- larger orbital speeds
- the same period
General
✓✗A planet has half the mass and half the radius of the earth. If a body weighs 100 N on the earth, its weight on the planet is
- 400 N
- 50 N
- 200 N
- 100 N
General
✓✗Two spheres of masses 10 kg and 20 kg have their centres 1 m apart. The gravitational force between them is about
- 200 N
- 1.33 × 10−11 N
- 1.33 × 10−8 N
- 6.67 × 10−11 N
General
✓✗The acceleration due to gravity on the surface of the earth is given by
- \( g = \dfrac{GM}{R^2} \)
- \( g = \dfrac{GR^2}{M} \)
- \( g = \dfrac{GM}{R} \)
- \( g = GMR^2 \)
General
✓✗Assertion: The gravitational potential is maximum (least negative) at infinity.
Reason: The gravitational potential at any point near a mass is negative.
Reason: The gravitational potential at any point near a mass is negative.
- 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 total energy of a satellite of mass 200 kg in a circular orbit is −4 × 109 J. Its kinetic energy is
- 2 × 109 J
- 4 × 109 J
- 8 × 109 J
- −8 × 109 J
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
✓✗The value of g at a depth d is equal to its value at a height h = R above the surface. Then d is (R = earth's radius)
- R
- \( \dfrac R2 \)
- \( \dfrac{3R}{4} \)
- \( \dfrac R4 \)
General
✓✗The escape velocity from the earth's surface is v. The escape velocity from the surface of another planet having a radius four times that of the earth and the same mass density is
- 3v
- 2v
- v
- 4v
General
✓✗If the radius of the earth shrank to half with its mass unchanged, the escape speed would become
- \( \sqrt2 \) times
- 4 times
- 2 times
- half
General
✓✗Statement I: A body at the earth's surface needs less energy to escape from the earth if it is first put in a circular orbit.
Statement II: The total energy needed to escape from the surface does not depend on the route taken.
Statement II: The total energy needed to escape from the surface does not depend on the route taken.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
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
✓✗Inside a uniform thin spherical shell of mass M and radius R, the gravitational potential is
- constant, equal to −GM/R
- varies as 1/r
- zero
- varies as r