## Newtonian Gravitation And Planetary Motion Multiple Choice Questions And Answers

**Question 1. The density of the earth is about**

- \(\frac{1}{5.5}\) times the density of water
- 2 times the density of water
- 5.5 times the density of water
- 10 times the density of water

**Answer:** 3. 5.5 times the density of water

**Question 2. A body of mass m is divided into two parts. The mass of one part is xm and that of the other part is (1- x) m. For a definite distance of separation between them, if the gravitational force of attraction has to be the maximum, the value of x should be**

- \(\frac{1}{2}\)
- \(\frac{1}{4}\)
- \(\frac{1}{\sqrt{2}}\)
- \(\frac{\sqrt{3}}{2}\)

**Answer:** 1. \(\frac{1}{2}\)

**Question 3. Two bodies of masses m _{1} and m_{2} are initially at rest and an infinite distance apart. Due to mutual attraction, they approach each other. When they are r distance apart, their relative velocity of approach is**

- \(\left[\frac{2 G\left(m_1+m_2\right)}{r}\right]^{1 / 2}\)
- \(\left[\sqrt{\frac{2 G}{r}}\left(\frac{m_1+m_2}{2}\right)\right]^{1 / 2}\)
- \(\left[\frac{r}{2 G\left(m_1 \cdot m_2\right)}\right]^{1 / 2}\)
- \(\left[\frac{2 G}{r} \cdot\left(m_1 m_2\right)\right]^{1 / 2}\)

**Answer:** 1. \(\left[\frac{2 G\left(m_1+m_2\right)}{r}\right]^{1 / 2}\)

**Question 4. Gravitational force is**

- Repulsive
- Conservative
- Electrical
- Non-conservative

**Answer:** 3. Electrical

**Question 5. Two small but heavy spheres of mass M each are kept at a distance r on a horizontal plane. The magnitude of the gravitational potential at the mid-point of the line joining the centres of the two spheres will be**

- Zero
- –\(\frac{G M}{r}\)
- –\(\frac{2G M}{r}\)
- –\(\frac{4G M}{r}\)

**Answer:** 4. –\(\frac{4G M}{r}\)

**Question 6. An infinite number of masses, each of mass M, are placed along a straight line at distances of R, 2R,4R, 8 R, etc. from a reference point O. The magnitude of the gravitational potential at point O will be**

- \(\frac{G M}{2 R}\)
- \(\frac{G M}{R}\)
- \(\frac{2 G M}{R}\)
- \(\frac{3 G M}{4 R}\)

**Answer:** 3. \(\frac{2 G M}{R}\)

**Question 7. In the case of a freely falling spherical body, its acceleration due to gravity depends on**

- Mass of the body
- Radius of the body
- Density of the material of the body
- None of the above

**Answer:** 4. None of the above

**Question 8. If the earth is assumed to be a sphere of radius R, the height above the surface of the earth where the value of the acceleration due to gravity will be half its value on the earth’s surface is**

- h = \(\frac{R}{2}\)
- h = \(\frac{R}{\sqrt{2}}\)
- h = (√2 + 1)R
- h = (√2 – 1)R

**Answer:** 4. h = (√2 – 1)R

**Question 9. The mass of a planet is 4 times the mass of the earth and its radius is 2 times the radius of the earth. The acceleration due to gravity on that planet is**

- 9.8 m · s
^{-2} - 19.6 m · s
^{-2} - 4.9 m · s
^{-2} - 39.2 m · s
^{-2}

**Answer:** 1. 9.8 m · s^{-2}

**Question 10. The mass of the moon is 1/10 th of that of the earth and the radius of the moon is 1/4 th of that of the earth. The ratio of the acceleration due to gravity on the moon and that on the earth is**

- 2:1
- 1:2
- 1:5
- 5:1

**Answer:** 3. 1:5

**Question 11. If the diurnal motion of the earth ceases all of a sudden, then the value of the acceleration due to the gravity of a body at the equator will**

- Remain the same
- Be zero
- Increase
- Decrease

**Answer:** 3. Increase

**Question 12. Keeping the mass of the earth constant, if the radius of the earth is made 80% of its present value, the acceleration due to gravity on the earth’s surface would**

- Remain unchanged
- Decrease by 36% (approx.).
- Increase by 36% (approx.)
- Increase by 56% (approx.)

**Answer:** 4. Increase by 56% (approx.)

**Question 13. If the radius of the earth is R, the height above the face of the earth where the acceleration due to gravity will be 1 % of its value on the earth’s surface is**

- 8 R
- 9R
- 10 R
- 20 R

**Answer:** 2. 9R

**Question 14. If the change in the acceleration due to gravity (g) at an altitude h above the earth’s surface is equal to the change in g at a depth x below the earth’s surface [assume that both x and h are significantly smaller than the radius of the earth, then**

- x = h
- x = 2h
- x = \(\frac{h}{2}\)
- x = h²

**Answer:** 2. x = 2h

**Question 15. The acceleration due to gravity on the surface of the earth is 9.8 m · s ^{-2}. The size of a planet is the same as that of the Earth, but its density is twice the density of the Earth. The value of the acceleration due to gravity on that planet is**

- 19.6 m · s
^{-2} - 9.8 m · s
^{-2} - 4.9 m · s
^{-2} - 2.45 m · s
^{-2}

**Answer:** 1. 19.6 m · s^{-2}

**Question 16. A rocket is projected vertically upwards from the surface of the earth (radius = R) with a velocity v. To what height will the rocket rise? (Neglect air friction)**

- \(h=\frac{R}{\left(\frac{2 g R}{v^2}-1\right)}\)
- \(h=\frac{R}{\left(\frac{2 g R}{\nu^2}+1\right)}\)
- \(h=R\left(\frac{2 g R}{v^2}-1\right)\)
- \(h=R\left(\frac{2 g R}{v^2}+1\right)\)

**Answer:** 1. \(h=\frac{R}{\left(\frac{2 g R}{v^2}-1\right)}\)

**Question 17. If one moves from the equator to the pole, the value of g**

- Remains unchanged
- Decreases
- Increases
- Increases first and then decreases

**Answer:** 3. Increases

**Question 18. If the radius of the earth were to shrink by 1%, its mass remaining the same, the acceleration due to gravity on the surface of the earth would**

- Increase
- Decrease
- Remain unchanged
- Be zero

**Answer:** 1. Increase

**Question 19. If G is the universal gravitational constant and g is the acceleration due to gravity then the unit of the quantity \(\frac{G}{g}\) is**

- kg · m
^{2} - kg/m
- kg/m
^{2} - m
^{2}/kg

**Answer:** 4. m^{2}/kg

**Question 20. 20. At what altitude (h) above the earth’s surface would the acceleration due to gravity be one-fourth of its value at the earth’s surface? Where R is the radius of the earth.**

- h =R
- h =4R
- h =2R
- h = 16R

**Answer:** 1. h = R

**Question 21. A planet has the same density and acceleration due to gravity as of earth and the universal gravitational constant G is twice of Earth. The ratio of thin radii is**

- 1:4
- 1:5
- 1:2
- 3:2

**Answer:** 3. 1:2

**Question 22. The escape velocity from the earth is v _{e}. If both the mass and the radius of a planet are twice that of the Earth, then the escape velocity from that planet will be**

- v
_{e} - 2v
_{e} - 4v
_{e} - 16v
_{e}

**Answer:** 1. v_{e}

**Question 23. The escape velocity of a particle of mass m is**

- Directly Proportional To m²
- Directly Proportional To m
- Direcdy Proportional To m
^{0} - Directly Proportional To m
^{-1}

**Answer:** 3. Direcdy Proportional To m^{0}

**Question 24. The value of the escape velocity of a body thrown vertically upwards from the surface of the earth is v. If the body is thrown making an angle θ with the vertical, then the value of the escape velocity will be**

- v
- vcosθ
- vsinθ
- vtanθ

**Answer:** 1. v

**Question 25. The value of the escape velocity from the earth is v _{e}. If the radius of a planet is 4 times that of the Earth and its density is 9 times the density of the Earth, then the value of the escape velocity from that planet will be**

- 6v
- 12v
- 20v
- 36v

**Answer:** 2. 12v

**Question 26. The escape velocity of a planet is v _{e}. From this planet a particle is projected upwards with a velocity v. The particle will revolve like a satellite if**

- \(\frac{v_e}{\sqrt{2}}<v<2 v_e\)
- \(\frac{v_e}{v_2}<v<v_e\)
- \(v_e<v<\sqrt{2} v_e\)
- \(\frac{v_e}{v_2}<v<\frac{v_e}{2}\)

**Answer**: 2. \(\frac{v_e}{v_2}<v<v_e\)

**Question 27. Escape speed on the surface of a planet varies with the mass m of a body as**

- m
^{0} - m
- m
^{-1} - m
^{2}

**Answer:** 1. m^{0}

**Question 28. The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth’s mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become**

- 5.6 km · s
^{-1} - 11.2km · s
^{-1} - 44.8 km · s
^{-1} - 22.4 km · s
^{-1}

**Answer:** 4. 22.4 km · s^{-1}

**Question 29. Keeping the mass constant, if the radius of the earth is halved, then the span of a day**

- Will decrease
- Will increase
- Will remain unchanged
- No conclusion can be arrived at

**Answer:** 1. Will decrease

**Question 30. The weight of a body on the surface of the earth is W. The weight of that body at an altitude equal to half the radius of the earth will be**

- \(\frac{W}{2}\)
- \(\frac{2W}{3}\)
- \(\frac{4W}{9}\)
- \(\frac{W}{4}\)

**Answer:** 3. \(\frac{4W}{9}\)

**Question 31. A planet in elliptical orbit around a star moves form the point in its orbit furthest from the star to the closest point. The work done by the force of gravity during this movement is**

- Zero
- Positive
- Negative
- Infinite

**Answer**: 3. Negative

**Question 32. The height of a geostationary satellite from the surface of the earth is**

- 100 km
- 5 km
- 36000 km
- 2 x 10
^{5}km

**Answer:** 3. 36000 km

**Question 33. Two satellites of masses m _{1} and m_{2} (m_{1 }> m_{2}) are revolving around the earth in orbits of radii r_{1} and r_{2} (r_{1 }> r_{2}) velocities v_{1 }and v_{2} respectively. In this case**

- v
_{1}= v_{2} - v
_{1}< v_{2} - v
_{1}> v_{2} - \(\frac{v_1}{r_1} = {v_2}{r_2}\)

**Answer:** 2. v_{1} < v_{2}

**Question 34. Two satellites A and B are revolving along circular paths of the same radius. The mass of A is 16 times the mass of B. The ratio of the period of revolution of B to that of A is**

- 1:16
- 1:4
- 1:2
- 1:1

**Answer:** 4. 1:1

**Question 35. Two planets are revolving around the sun. Their time periods of revolution and the average radii of the orbits are respectively (T _{1}, T_{2}) and (r_{1}, r_{2}). The ratio T_{1}/T_{2} is**

- \(\left(\frac{r_1}{r_2}\right)^{1 / 2}\)
- \(\frac{r_1}{r_2}\)
- \(\left(\frac{r_1}{r_2}\right)^2\)
- \(\left(\frac{r_1}{r_2}\right)^{3 / 2}\)

**Answer:** 4. \(\left(\frac{r_1}{r_2}\right)^{3 / 2}\)

**Question 36. The centripetal force necessary for an artificial satellite revolving along its orbit around the earth is delivered by**

- The combustion of the engine fuel
- The ejection of exhausted hot gas
- The gravitational attraction of the sun
- The gravitational attraction of the earth

**Answer:** 4. The gravitational attraction of the earth

**Question 37. Keeping the sun at the focus, a planet revolves around the sun in an elliptical orbit. The shaded areas shown are equal, but the path DC is less than the path AB. If the time taken by the planet to go from A to B is t _{1}, and that from C to D is t_{2}, then**

- t
_{1}< t_{2} - t
_{1}> t_{2} - t
_{1}= t_{2} - t
_{1}= 3t_{2}

**Answer:** 3. t_{1} = t_{2}

**Question 38. The radii of the orbits of two satellites A and B revolving around a planet are 4R and R respectively. If the velocity of A is 3 v, the velocity of B will be**

- \(\frac{4}{3}\) v
- \(\frac{3}{2}\) v
- 6v
- 12v

**Answer:** 3. 6v

**Question 39. In the case of the motion of a planet**

- The orbital velocity in its orbit remains constant
- The orbital angular velocity remains constant
- The total angular momentum remains constant
- The orbital radius remains constant

**Answer:** 3. The total angular momentum remains constant

**Question 40. Two small artificial satellites are revolving around the earth in two circular orbits of radii r and (r+Δr). If their time periods of revolution are T and T+ ΔT, then(Δr<<1, ΔT<<T)**

- \(\Delta T=\frac{3}{2} T \frac{\Delta r}{r}\)
- \(\Delta T=-\frac{3}{2} T \frac{\Delta r}{r}\)
- \(\Delta T=\frac{2}{3} T \frac{\Delta r}{r}\)
- \(\Delta T=T \cdot \frac{\Delta r}{r}\)

**Answer:** 1. \(\Delta T=\frac{3}{2} T \frac{\Delta r}{r}\)

**Question 41. If the gravitational force is inversely proportional to the n-th power of the distance, then the time period of the revolution of a planet around the sun in a circular orbit of radius R will be**

- Directly proportional to \(R^{\frac{1}{2}(n+1)}\)
- Directly proportional to \(R^{\frac{1}{2^{(n-1)}}}\)
- Directly proportional to \(R^n\)
- Directly proportional to \(R^{\frac{1}{2}(n-2)}\)

**Answer:** 1. Directly proportional to \(R^{\frac{1}{2}(n+1)}\)

**Question 42. A satellite of mass m is revolving around the earth at a height x above the surface of the earth. The radius of the earth is R. If the acceleration due to gravity is g, the orbital speed of the satellite will be**

- gx
- \(\frac{g R}{R-x}\)
- \(\frac{g R^2}{R+x}\)
- \(\left(\frac{g R^2}{R+x}\right)^{1 / 2}\)

**Answer:** 3. \(\frac{g R^2}{R+x}\)

**Question 43. The ratio of the magnitudes of the kinetic energy and the potential energy of an artificial satellite revolving around the Earth is**

- 1:2
- 1:√2
- 2:1
- √2:1

**Answer:** 1. 1:2

**Question 44. Kepler’s second law is the consequence of the law of conservation of**

- Linear momentum
- Energy
- Angular momentum
- Mass

**Answer:** 3. Angular momentum

**Question 45. A satellite is moving in an orbit around a planet with kinetic energy k and potential energy v. The satellite will escape from the gravitational pull of the planet if its kinetic energy becomes**

- Half
- Double
- Three times
- Four times

**Answer:** 2. Double

**Question 46. The angle between the equatorial plane and the orbital plane of a geostationary satellite is:**

- 0°
- 60°
- 90°
- 120°

**Answer:** 1. 0°

**Question 47. The angle between the equatorial plane and the orbital plane of a polar satellite is**

- 0°
- 90°
- 120°
- 180°

**Answer:** 2. 90°

**Question 48. A geostationary satellite orbits around the earth’s surface in a circular orbit of radius 36,000 km. Then, the time period of a spy satellite orbiting seventeen hundred kilometres above the earth’s surface (R _{e} = 6400 km ) will approximately be**

- 1/2 h
- 1h
- 2h
- 4h

**Answer:** 3. 2h

**Question 49. An artificial satellite moving in a circular orbit around the earth has a total energy -E _{0}. Its potential energy is**

- -E
_{0} - 1.5 E
_{0} - -2 E
_{0} - E
_{0}

**Answer:** 3. -2 E_{0}

**Question 50. The reason of weightlessness in a satellite is**

- Zero gravity
- No atmosphere
- Zero reaction force by satellite surface
- None of the above

**Answer:** 3. Zero reaction force by satellite surface

**Question 51. A body projected vertically from the Earth reaches a height equal to the Earth’s radius before returning to the earth. The power exerted by the gravitational force is greatest**

- At the instant just before the body hits the earth
- It remains constant all through
- At the instant just after the body is projected
- At the highest position of the body

**Answer:** 1. At the instant just before the body hits the earth

**Question 52. An orbiting satellite has**

- Only Kinetic Energy
- Only Potential Energy
- Kinetic And Potential Energy
- Zero Energy

**Answer:** 3. Kinetic And Potential Energy

**Question 53. If the daily rotation of the earth ceases suddenly, then the weight of a body situated at the north pole will**

- Zero
- Remain the same
- Increase
- Decrease

**Answer:** 2. Remain the same

**Question 54. In the case of a freely falling body, which of the graphs will indicate accurately the distance vs time variation? (air resistance is neglected)**

**Answer:** 1.

**Question 55. The radius of a uniform sphere is R and its mass is M. The values of the gravitational intensity at distances r _{1} and r_{2} from the centre of the sphere are F_{1} and F_{2} respectively. Then,**

- \(\frac{F_1}{F_2}=\frac{r_1}{r_2}, if r_1<R\) and \(r_2<R\)
- \(\frac{F_1}{F_2}=\frac{r_1^2}{r_2^2}, if r_1>R\) and \(r_2>R\)
- \(\frac{F_1}{F_2}=\frac{r_1}{r_2}, if r_1>R\) and \(r_2>R\)
- \(\frac{F_1}{F_2}=\frac{r_1^2}{r_2^2}, if r_1<R\) and \(r_2<R\)

**Answer:** 1. \(\frac{F_1}{F_2}=\frac{r_1}{r_2}, if r_1<R\) and \(r_2<R\)

**Question 56. The dimensional formula of gravitational field intensity is**

- MLT
^{-1} - MLT
^{-2} - M
^{0}LT^{-2} - M
^{0}L^{2}T^{-1}

**Answer:** 3. M^{0}LT^{-2}

**In this type of question, more than one option is correct.**

**Question 57. An orbiting satellite will escape if**

- Its speed is increased by 41%
- Its speed in the orbit is made \(\sqrt{(1.5)}\) times of its initial value
- Its kinetic energy is doubled
- It stops moving in the orbit

**Answer:**

1. Its speed is increased by 41%

3. Its kinetic energy is doubled

**Question 58. A comet revolves around the sun in a highly elliptical orbit. Which of the following will remain constant throughout its orbit?**

- Kinetic energy
- Potential energy
- Total energy
- Angular momentum

**Answer:**

3. Total energy

4. Angular momentum

**Question 59. Which of the following is correct?**

- Out of electrostatic, electromagnetic, nuclear and gravitational interactions, the gravitational interaction is the weakest
- If Earth were to rotate faster than its present speed, the weight of an object would decrease at the equator but remain unchanged at the poles
- The mass of the earth in terms of g, R and g is (gR²/G)
- If Earth stops rotating in its orbit around the sun there will be no variation in the weight of a body on the surface of Earth

**Answer:**

**Question 60. A small mass m is moved slowly from the surface of the earth to a height h above the surface. The work done (by an external agent) in doing this is**

- mgh, for all values of h
- mgh, for h << R
- 1/2 mgR, for h = R
- -1/2 mgR, for h = R

**Answer:**

2. mgh, for h << R

3. 1/2 mg R, for h = R