1.State the universal law of gravitation.
Ans: The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The magnitude of the gravitational force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it is expressed as:
where:
F is the gravitational force between the objects,
G is the gravitational constant,
m1 and m2 are the masses of the two objects,
r is the distance between the centers of the two objects.
2. Write the formula to find the magnitude of the gravitational force between the Earth and an object on the surface of the Earth.
Ans:
Consider FF as the gravitational force of attraction between the object and the Earth.
Let mm be the mass of the object on the surface of the Earth, and MM be the mass of the Earth.
The distance between the Earth’s center and the object is the radius of the Earth, RR.
According to the universal law of gravitation, the magnitude of the gravitational force between the Earth and an object on the surface of the Earth is given by:
where:
G is the gravitational constant,
M is the mass of the Earth,
m is the mass of the object,
R is the radius of the Earth.
3. Write the formula to find the magnitude of the gravitational force between the Earth and an object on the surface of the Earth.
Ans:
Consider FF as the gravitational force of attraction between the object and the Earth.
Let mm be the mass of the object on the surface of the Earth, and MM be the mass of the Earth.
The distance between the Earth’s center and the object is the radius of the Earth, RR.
According to the universal law of gravitation, the magnitude of the gravitational force between the Earth and an object on the surface of the Earth is given by:
where:
G is the gravitational constant,
M is the mass of the Earth,
m is the mass of the object,
R is the radius of the Earth.
4. What do you mean by free fall?
Ans: Free fall refers to the motion of an object when it is solely under the influence of Earth’s gravitational force. When an object is dropped from a certain height, it accelerates towards the surface of the Earth due to gravity, without any other forces (like air resistance) acting on it. This downward movement of the object is called free fall.
5. What do you mean by acceleration due to gravity?
On the surface of the Earth, the value of acceleration due to gravity is approximately:
6.What are the differences between the mass of an object and its weight?
Ans: The differences between the mass of an object and its weight are tabulated below.
7. Why is the weight of an object on the moon 1/6th its weight on the earth?
Ans: The weight of an object on the Moon is 1/6th of its weight on Earth due to the difference in the Moon’s mass and radius compared to the Earth. The mass of the Moon is about 1/100th of the Earth’s mass, and its radius is about 1/4th that of the Earth. Gravitational force is directly proportional to the mass of the celestial body and inversely proportional to the square of its radius. Therefore, the gravitational attraction on the Moon is about one-sixth that of Earth’s, causing the weight of an object on the Moon to be one-sixth of its weight on Earth. The Moon’s smaller mass and radius result in weaker gravitational force compared to Earth.
8. Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Ans: It is difficult to carry a school bag with a thin strap because of the pressure exerted on the shoulders. Pressure is defined as the force applied per unit area. When the surface area over which the force acts is small, the pressure becomes larger. In the case of a thin strap, the surface area in contact with the shoulder is small, which increases the pressure. As a result, the pressure on the shoulder becomes quite high, making it uncomfortable to carry the bag for extended periods.
9. What do you mean by buoyancy?
Ans: Buoyancy is the upward force exerted by a liquid on an object that is immersed in it. This force is what allows objects to float or rise when placed in a fluid, and it acts in the opposite direction of gravity. The magnitude of the buoyant force depends on the volume of the displaced fluid and its density.
Ans: An object floats or sinks in water based on its density relative to that of water:
(i) If the density of the object is greater than that of water, the object sinks. This is because the object cannot displace enough water to counteract its weight, causing it to sink.
(ii) If the density of the object is less than that of water, the object floats. The buoyant force from the water is sufficient to counteract the object’s weight, allowing it to stay on the surface.
Ans: A weighing machine measures your weight, but it is calibrated to display your mass. When you stand on the weighing machine, the downward force of your weight is counteracted by the upward buoyant force of the air. This causes your apparent weight to be slightly less than your actual weight. Since the machine uses the apparent weight to estimate mass, the mass shown on the scale (42 kg) is slightly less than your true mass. Therefore, your actual mass is a bit more than 42 kg.
Ans: In reality, the iron bar is heavier than the cotton bag. Although both the cotton bag and the iron bar show a mass of 100 kg on the weighing machine, the actual weights are different due to the buoyant force exerted by the air.
The cotton bag, being less dense than the iron bar, has a larger volume. This means it displaces more air, which leads to a larger buoyant force (upthrust). Since the upthrust reduces the apparent weight measured by the scale, the cotton bag’s apparent weight is less than its true weight. On the other hand, the iron bar, with its smaller volume, experiences less upthrust.
Therefore, the true weight of the cotton bag is actually more than the true weight of the iron bar, because the larger upthrust experienced by the cotton bag makes its apparent weight less than its actual weight.