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Q1. The distance 3.84 × 10⁵ km is equal to
To convert km to m, multiply by 1000. 3.84 × 10⁵ km = 3.84 × 10⁵ × 10³ = 3.84 × 10⁸ m.
Q2. The gravitational force on a body of mass m is
The gravitational force on a body of mass m near the Earth’s surface is given by F = mg, where g is the acceleration due to gravity.
Q3. The value of g is smaller at the
The value of g is smaller at the equator than at the poles because the Earth is not a perfect sphere (it is flattened at the poles) and also due to the centrifugal effect of Earth’s rotation.
Q4. Acceleration due to gravity is caused by
Acceleration due to gravity (g) is caused by the Earth’s gravitational pull. It is the acceleration experienced by any object due to the force of gravity.
Q5. The formula used to calculate gravitational force is
The universal law of gravitation gives the formula F = GMm/d², where G is the universal gravitational constant, M and m are masses, and d is the distance between their centres.
Q6. The SI unit of G is
From F = GMm/d², we get G = Fd²/Mm. The SI unit of G is N·m²/kg² or N m² kg⁻².
Q7. Free fall occurs when an object falls under the influence of
Free fall is the motion of an object where gravity is the only force acting upon it. Air resistance is neglected in free fall.
Q8. For objects far from the earth, g depends on
For objects far from the Earth, g = GM/r², where r is the distance from the Earth’s centre. So g depends on the distance from the Earth.
Q9. The acceleration of a freely falling object is due to
A freely falling object accelerates due to Earth’s gravitational force. This acceleration is denoted by g and is approximately 9.8 m/s² near the Earth’s surface.
Q10. The distance between the earth and the moon is
The average distance between the Earth and the Moon is approximately 3.84 × 10⁵ km or 3.84 × 10⁸ m.
Q11. The acceleration due to gravity is denoted by
The acceleration due to gravity is denoted by the symbol ‘g’. Its value near the Earth’s surface is approximately 9.8 m/s².
Q12. The gravitational force near the earth is maximum at
The gravitational force is maximum at the poles because the Earth is slightly flattened, making the distance from the centre less at the poles, and the centrifugal effect is zero.
Q13. For objects on the surface of the earth, distance d is equal to
For objects on the Earth’s surface, the distance d in the gravitation formula is the radius of the Earth (R). So F = GMm/R².
Q14. According to the second law of motion, force equals
Newton’s second law states that Force = Mass × Acceleration, or F = ma.
Q15. One phenomenon explained by gravitation is
Gravitation explains many phenomena, including why we are bound to the Earth, the motion of planets, tides, and the falling of objects.
Q16. The force mg acts
The force mg (weight) acts vertically downward towards the centre of the Earth. It is the gravitational force acting on an object.
Q17. The mass of the moon given in the example is
The mass of the moon is approximately 7.4 × 10²² kg. This is often used in calculations involving the Earth-moon system.
Q18. The expression g = GM/R² is valid
The formula g = GM/R² is valid for points on or near the Earth’s surface, where R is the radius of the Earth.
Q19. The SI unit of acceleration due to gravity is
The SI unit of acceleration due to gravity is metres per second squared (m/s² or m s⁻²), the same as the unit of acceleration.
Q20. Acceleration due to gravity is independent of
Acceleration due to gravity (g) is independent of the mass of the falling object. All objects fall with the same acceleration g, regardless of their mass (ignoring air resistance).
Q21. Throwing a stone upward and letting it fall is an example of
When a stone is thrown upward and falls back down under the influence of gravity alone (ignoring air resistance), it is an example of free fall during the downward motion.
Q22. The earth is
The Earth is not a perfect sphere; it is an oblate spheroid, meaning it is slightly flattened at the poles and bulging at the equator.
Q23. Free fall does not include the effect of
Free fall is the motion of an object where only gravity acts on it. Air resistance is neglected in the ideal free fall model.
Q24. During free fall, the direction of motion
During free fall, the direction of motion remains the same (downward towards the Earth), though the speed increases due to acceleration.
Q25. In the formula g = GM/d², M represents
In the formula g = GM/d², M represents the mass of the Earth, and d is the distance from the Earth’s centre.
Q26. At the highest point of motion, the velocity of the stone is
When a stone is thrown upward, at the highest point its velocity becomes zero instantaneously before it starts falling back down.
Q27. Equation F = mg represents
F = mg represents the gravitational force (weight) acting on an object of mass m near the Earth’s surface.
Q28. When an object is thrown upward, its velocity initially
When an object is thrown upward, its initial velocity decreases due to the acceleration of gravity acting in the opposite direction. It slows down until it reaches the highest point.
Q29. The radius of earth is denoted by
The radius of the Earth is commonly denoted by the symbol R. Its value is approximately 6.37 × 10⁶ m.
Q30. The unit of force mg is
Force mg (weight) is measured in newtons (N) because it is a force. 1 N = 1 kg·m/s².
Q31. The mass of the earth given in the example is
The mass of the Earth is approximately 6 × 10²⁴ kg. This value is commonly used in gravitational calculations.
Q32. A change in velocity implies
Acceleration is defined as the rate of change of velocity. Any change in velocity (speed or direction) implies acceleration.
Q33. The acceleration due to gravity decreases as distance
Since g = GM/r², as the distance r from the Earth’s centre increases, g decreases. So g is inversely proportional to the square of the distance.
Q34. Even at the highest point, acceleration due to gravity is
At the highest point of motion, the velocity is zero, but the acceleration due to gravity is still acting downward with magnitude g. Gravity never stops acting.
Q35. For objects on the earth’s surface, acceleration due to gravity is
For objects on the Earth’s surface, the acceleration due to gravity is given by g = GM/R², where R is the radius of the Earth.
Q36. The gravitational force between earth and moon acts
The gravitational force between the Earth and the Moon acts along the line joining their centres. This is true for all gravitational forces between objects.
Q37. Tides are caused due to the gravitational effect of
Tides are caused primarily by the gravitational pull of the Moon and, to a lesser extent, the Sun. The combined effect of these celestial bodies causes ocean tides.
Q38. The force exerted by the earth on the moon is
Using F = GMm/d² with Earth’s mass (6 × 10²⁴ kg), Moon’s mass (7.4 × 10²² kg), and distance (3.84 × 10⁸ m), we get F ≈ 2.02 × 10²⁰ N.
Q39. The gravitational force depends on
The gravitational force depends on the masses of the objects and the distance between them. It does not depend on colour, shape, or volume.
Q40. During free fall, the magnitude of velocity
During free fall, the object accelerates downward due to gravity, so the magnitude of velocity increases continuously.
Q41. Another phenomenon explained by gravitation is the motion of
The motion of the Moon around the Earth is explained by gravitation. The Earth’s gravitational force provides the necessary centripetal force.
Q42. Gravitational force always acts
Gravitational force always acts towards the Earth (or towards the centre of the attracting body). For objects near Earth, this is downward.
Q43. The value of g is greater at
The value of g is greater at the poles than at the equator because the Earth is flattened at the poles and the centrifugal effect is absent there.
Q44. For most calculations near the earth, g is considered
For most calculations near the Earth’s surface, g is considered constant at approximately 9.8 m/s². This simplification is used for practical purposes.
Q45. The radius of the earth is greatest at the
The Earth bulges at the equator due to its rotation, so the radius of the Earth is greatest at the equator and smallest at the poles.
Q46. The universal law of gravitation explains
The universal law of gravitation explains several natural phenomena including the motion of planets, the falling of objects, tides, and the motion of the Moon.
Q47. Free fall motion is an example of
Free fall near the Earth’s surface is an example of uniform acceleration because the acceleration due to gravity (g) is approximately constant.
Q48. The motion of planets around the Sun is explained by
The motion of planets around the Sun is explained by gravitation. The Sun’s gravitational pull provides the centripetal force keeping planets in their orbits.
Q49. By equating gravitational force expressions, we get
By equating F = mg (weight) and F = GMm/d² (universal gravitation), we get mg = GMm/d². Cancelling m gives g = GM/d².
Q50. The value of the universal gravitational constant G used is
The value of the universal gravitational constant G is 6.7 × 10⁻¹¹ N·m²/kg². This is the value commonly used in calculations involving gravitation.