Answer the following questions.

(a) What is the difference between mass and weight of an object? Will the mass and weight of an object on the earth be the same as their values on Mars? Why?

Answer: Mass is the amount of matter in an object. It is a measure of inertia, which is the resistance of an object to change its motion. Mass is a scalar quantity, which means it has magnitude but no direction.

Weight is the force of gravity acting on an object. It is a measure of the force that pulls the object towards the center of the Earth. Weight is a vector quantity, which means it has magnitude and direction.

The mass of an object is the same everywhere in the universe. However, the weight of an object can change depending on the strength of gravity. For example, an object will weigh less on Mars than it does on Earth because the gravity on Mars is weaker.

So, the mass and weight of an object on the Earth will not be the same as their values on Mars. The mass of the object will be the same, but the weight of the object will be less on Mars.

Here is a table that summarizes the difference between mass and weight:

Property	Mass	Weight
Definition	Amount of matter in an object	Force of gravity acting on an object
Units	kilogram (kg)	newton (N)
Direction	None	Downward
Dependence on gravity	No	Yes

(b) What are (i) free fall, (ii) acceleration due to gravity (iii) escape velocity (iv) centripetal force?
Answer:
(i) Free fall:
Free fall is the motion of an object under the influence of gravity alone. In free fall, the object is not acted upon by any other forces, such as air resistance

(ii) acceleration due to gravity: Acceleration due to gravity is the acceleration that an object experiences due to the force of gravity. It is the rate at which the object’s velocity changes as it falls towards the Earth.

The acceleration due to gravity on Earth is approximately 9.8 meters per second squared (m/s²). This means that an object falling towards the Earth will accelerate at a rate of 9.8 m/s². In other words, its velocity will increase by 9.8 m/s every second.

The acceleration due to gravity is not the same everywhere in the universe. It is stronger on planets with more mass, and weaker on planets with less mass. For example, the acceleration due to gravity on the Moon is about 1.6 m/s², which is about one-sixth of the acceleration due to gravity on Earth.

 

(iii) Escape velocity: Escape velocity is the minimum velocity that an object needs to escape from the gravitational pull of a planet or other celestial body.

The escape velocity depends on the mass of the planet and the distance from the centre of the planet. The escape velocity on Earth is about 11.2 kilometres per second. This means that an object needs to be thrown upwards with a velocity of at least 11.2 kilometres per second in order to escape from the Earth’s gravity.

Once an object has reached escape velocity, it will continue to move upwards forever. It will not fall back to the planet.

The escape velocity is a very important concept in space travel. It is the minimum velocity that a rocket needs to reach in order to escape from the Earth’s gravity and travel to other planets.

 

(iv) Centripetal force:

Centripetal force is the force that keeps an object moving in a circular path. It is directed towards the centre of the circle.

The centripetal force is needed to counteract the centrifugal force, which is the tendency of an object to fly off in a straight line.

The centripetal force can be provided by gravity, tension, or friction. For example, the centripetal force that keeps a satellite in orbit around the Earth is provided by gravity. The centripetal force that keeps a car moving in a circle on a racetrack is provided by friction between the tires and the road.

(c) Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?

Answer: The law of orbits: All planets move in elliptical orbits, with the Sun at one focus.

The law of areas: The radius vector joining a planet to the Sun sweeps out equal areas in equal intervals of time.

The law of harmonies: The square of the period of revolution of a planet is proportional to the cube of the semi-major axis of its orbit.

These laws were discovered by Johannes Kepler through careful observations of the planets. He did not know why the planets followed these laws, but he believed that they were the result of some underlying physical law.

Isaac Newton was able to explain Kepler’s laws using his theory of gravity. Newton’s theory states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is known as the inverse square law of gravity.

Newton showed that Kepler’s laws are a consequence of the inverse square law of gravity. In other words, the planets follow Kepler’s laws because they are orbiting the Sun under the influence of gravity.

(d) A stone is thrown vertically upwards with initial velocity u reaches a height ‘h’ before coming down. Show that the time taken to go up is same as the time taken to come down.

Answer.When a stone is thrown vertically upwards, it experiences the force of gravity, which acts downwards. The force of gravity causes the stone to accelerate downwards. However, the stone also has an initial velocity upwards. The initial velocity and the force of gravity act in opposite directions.

The stone will continue to move upwards until the force of gravity causes its velocity to become zero. At this point, the stone will stop moving upwards and will begin to fall downwards.

The time taken for the stone to go up is the same as the time taken for it to come down. This is because the force of gravity is the same in both directions. The only difference is that the velocity of the stone is in the opposite direction when it is coming down.

(e) If the value of g suddenly becomes twice its value, it will become two times more difficult to pull a heavy object along the floor. Why?

Answer. he force of gravity is what pulls us down to the Earth. It is also what makes it difficult to pull a heavy object along the floor. The greater the force of gravity, the more difficult it is to pull an object.

If the value of g suddenly becomes twice its value, it will become two times more difficult to pull a heavy object along the floor. This is because the force of gravity will be twice as strong.

Here is a simplified explanation:

• The force of gravity is what pulls us down to the Earth.
• The force of gravity is equal to the mass of the object times the acceleration due to gravity.
• If the acceleration due to gravity suddenly becomes twice its value, the force of gravity will also become twice its value.
• This means that it will be two times more difficult to pull an object against the force of gravity.

 

 class 10 Maharashtra board Gravitation Chapter 1 Exercise Question 3

Explain why the value of g is zero at the centre of the earth.

Answer. The acceleration due to gravity, or g, is the force that pulls us towards the center of the Earth. The value of g is highest at the surface of the Earth and decreases as we move towards the center of the Earth. At the center of the Earth, the value of g is zero.

This is because at the center of the Earth, there is no mass above us to pull us down. All of the mass of the Earth is equally distributed around us. So, the force of gravity from all of the mass cancels each other out, and the net force of gravity is zero.

Here is a simplified explanation:

• The acceleration due to gravity is the force that pulls us towards the center of the Earth.
• The force of gravity is caused by the mass of the Earth.
• The more mass an object has, the stronger the force of gravity it will exert.
• At the center of the Earth, there is no mass above us to pull us down.
• This is because all of the mass of the Earth is equally distributed around us.
• So, the force of gravity from all of the mass cancels each other out, and the net force of gravity is zero.

The acceleration due to gravity inside the Earth is not constant. It decreases as we move towards the center of the Earth. This is because the mass of the Earth is not uniformly distributed. The mass is concentrated in the core of the Earth.

The acceleration due to gravity at a distance d from the center of the Earth is given by the following formula:

g = G x M x (R – d)^2 / (R^2)

where:

• G is the gravitational constant
• M is the mass of the Earth
• R is the radius of the Earth
• d is the distance from the center of the Earth

As you can see, the acceleration due to gravity decreases as d increases. This is because the mass of the sphere of radius (R – d) decreases as d increases.

At the center of the Earth, d = R, so the acceleration due to gravity is zero. This is because there is no mass above us to pull us down. All of the mass of the Earth is equally distributed around us.

Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be 8–√T.

T= 2πGM√r3/2, where T = period of revolution of a planet around the Sun, M = mass of the Sun, G = gravitational constant and r = radius of the orbit assumed to be circular = distance of the planet from the Sun.
For r = R, T =T₁.