moltion

• The distance between two objects (d)

  The gravitational force (F) produced between them is inversely proportional to the square of the distance
• The gravitational force between two objects is given by Newton's law of gravitation: F ∝ 1/d^2
• The masses of two objects are doubled

  The gravitational force between them becomes four times greater
• The gravitational force between two objects depends only on their masses and the distance between them, not on the location (Earth or Moon)
• The value of acceleration due to gravity (g) decreases as the height above the surface of the Earth increases
• The value of g is slightly higher at the poles than at the equator due to the Earth's oblate shape and rotation effects
• The value of g decreases with height, so it is not highest at the highest place on Earth
• The distance between two objects (d)

  The gravitational force (F) produced between them
• Newton's law of gravitation


  F∝1/d^2
• The correct option is: (iii) F∝1/d^2
• The masses of two objects are doubled

  The gravitational force between them becomes four times greater
• If the gravitational force between two objects on Earth is 60 N, the gravitational force between those two objects on the moon is 60 N
• Statements about the value of acceleration due to gravity (g)

  • Increases as we go deeper from the surface of the earth (incorrect)
  • Decreases as the height above the surface of the earth increases (correct)
  • Is less in the polar region than that in the equatorial region (incorrect)
  • Is highest at the highest place on the Earth (incorrect)
• The correct option is: (ii) The value of acceleration due to gravity decreases as the height above the surface of the Earth increases
• Solving the questions step by step

  1. Step 1

  2. Step 2

  3. Step 3

  4. Step 4

  5. Step 5
• Weight

  Influenced by the acceleration due to gravity, which is highest at sea level and decreases with altitude and latitude
• Places where weight is measured

  • Peak of a mountain
  • Kechnakwal of Jhapa
• At higher altitudes, such as the peak of a mountain, you weigh less compared to lower altitudes
• Kechnakwal of Jhapa is at a lower altitude compared to the peaks of Mount Everest, Api Himal, and Chandragiri Hills
• Gravitational force (weight) at a height h from the Earth's surface

  F_h = F_0 * (R/(R+h))^2
• Given R = 6371 km and h = 6371 km, the weight of the object at a height of 6371 km from the surface of the earth is 200 N
• Acceleration due to gravity g


  g = GM/R^2
• If both the mass and the radius are doubled, the acceleration due to gravity g' = g/2 = 4.9 m/s^2
• Calculating weight on the Moon

  1. Weight on Earth = mg

  2. Weight on Moon = mg_m

  3. Mass m = Weight on Earth / g_Earth

  4. Weight on Moon = m * g_Moon
• The weight of a man on the moon, if his weight on earth is 750 N, is 124.74 N
• Weight on a planet

  W = mg = m * GM/R^2
• If the mass of planet B is twice the mass of planet A but its radius is half of the radius of planet A, and the mass of planet C is half of the mass of planet A but its radius is twice the radius of planet A, then the order of the weights is W_2 > W_1 > W_3
• Newton's universal law of gravitation


  Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers
• Gravitational force

  Always attractive
• Gravitational constant (G)

  Proportionality constant in Newton's law of universal gravitation<|>F = G * ((m1 * m2)/r^2)<|>F is the force of gravity between two objects<|>m1 and m2 are the masses of the two objects<|>r is the distance between the centers of the two objects<|>G is the gravitational constant (6.6743 × 10^-11 N⋅m²⋅kg⁻²)
• The value of the gravitational force will never be equal to the gravitational constant (G) itself
• Effects of gravitational force

  • It keeps us on Earth: The gravitational force between Earth and us creates our weight
  • It is responsible for the motion of celestial bodies: The gravitational force between the Sun and the planets causes the planets to orbit the Sun
  • It causes tides: The gravitational force of the Moon and the Sun on the Earth's oceans causes tides
  • It is responsible for the formation of stars and planets: The gravitational force pulls together large clouds of gas and dust, eventually leading to the formation of stars and planets
• If the mass of each object is doubled and the distance between them is quartered


  The new force of gravity (F2) is 16 times greater than the initial force (F1)
• Acceleration due to gravity (g)

  The acceleration that an object gains due to the force of gravity near the Earth's surface<|>Constant value of approximately 9.8 m/s^2
• Free fall


  The motion of an object under the influence of gravity only<|>Air resistance is negligible
• Objects in free fall

  • A skydiver falling before opening their parachute
  • An apple falling from a tree
• Conditions for free fall

  The only force acting on the object is gravity<|>Air resistance is negligible
• The feather and coin experiment, performed in a vacuum chamber, demonstrates that all objects regardless of mass fall at the same rate when air resistance is negligible
• Weightlessness


  The feeling of not experiencing a normal force due to gravity<|>Astronauts in space feel weightless because they are constantly falling around the Earth