Gravitation Worksheet10

Which is more fundamental, the mass of a body or its weight ? Why ?

How much is the weight of an object on the moon as compared to its weight on the earth ? Give reason for your answer.

(a) Define mass of a body. What is the SI unit of mass ?
(b) Define weight of a body. What is the SI unit of weight ?
(c) What is the relation between mass and weight of a body?

(a) State the universal law of gravitation. Name the scientist who gave this law.
(b) Define gravitational constant. What are the units of gravitational constant ?

(a) What do you understand by the term ‘acceleration due to gravity of earth’ ?
(b) What is the usual value of the acceleration due to gravity of earth ?
(c) State the SI unit of acceleration due to gravity.

(a) Is the acceleration due to gravity of earth 'g' a constant ? Discuss.
(b) Calculate the acceleration due to gravity on the surface of a satellite having a mass of 7.4 x 10^{22} kg and a radius of 1.74 × 10^{6} m (G = 6.7 × 10^{–11 }Nm^{2}/kg^{2}). Which satellite do you think it could be?

State and explain Kepler’s laws of planetary motion. Draw diagrams to illustrate these laws.

The mass of a planet is 6 × 10^{24} kg and its diameter is 12.8 × 10^{3} km. If the value of gravitational constant be 6.7 × 10^{–11} Nm^{2}/kg^{2}, calculate the value of acceleration due to gravity on the surface of the planet. What planet could this be?

If the distance between two masses is increased by a factor of 5, by what factor would the mass of one of them have to be altered to maintain the same gravitational force ? Would this be an increase or decrease in the mass ?

Universal law of gravitation states that every object exerts a gravitational force of attraction on every other object. If this is true, why don't we notice such forces ? Why don't the two objects in a room move towards each other due to this force ?

Suppose a planet exists whose mass and radius both are half those of the earth. Calculate the acceleration due to gravity on the surface of this planet.

A coin and a piece of paper are dropped simultaneously from the same height. Which of the two will touch the ground first ? What will happen if the coin and the piece of paper are dropped in vacuum ? Give reasons for your answer.

What is the actual shape of the orbit of a planet around the sun ? What assumption was made by Newton regarding the shape of an orbit of a planet around the sun for deriving his inverse square rule from Kepler's third law of planetary motion ?

The values of g at six distances A, B, C, D, E and F from the surface of the earth are found to be 3.08 m/s^{2}, 9.23 m/s^{2}, 0.57 m/s^{2}, 7.34 m/s^{2}, 0.30 m/s^{2} and 1.49 m/s^{2}, respectively.
Arrange these values of g according to the increasing distances from the surface of the earth (keeping the value of g nearest to the surface of the earth first)

Write the common unit of density.

What is the density of water in SI units?

What is the value of relative density of water?

Name the quantity whose one of the units is pascal (Pa).

State the units in which pressure is measured.

In which direction does the buoyant force on an object due to a liquid act?
Answer:

Mass

About onesixth (1/6)

a. The mass of a body is the quantity of matter (or material) contained in it. Mass is a scalar quantity which has only magnitude but no direction. The SI unit of mass is kilogram (kg).
b. The weight of a body is the force with which it is attracted towards the centre of the earth.
c. W = mg

The universal law of gravitation was given by Newton. So it is also known as Newton’s law of gravitation.
Statement: According to universal law of gravitational: Every body in the universe attract every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of force is along the line joining center of the two bodies.
The gravitational constant G is numerically equal to the force of gravitation which exists between two bodies of unit masses kept at a unit distance from each other. The value of universal gravitational constant G has been found to be 6.67 ´10^{–11} Nm^{2 }/ kg^{2}.

The uniform acceleration produced in a freely falling body due to the gravitational force of the earth is known as acceleration due to gravity and it is denoted by the letter g.
The value of g does not depend on the mass of the body. The value of g changes slightly from place to place but for most of the purpose it is taken as 9.8 m/s^{2}. Thus, the acceleration due to gravity, g = 9.8 m/s^{2}

(a) No (b) 1.63 m/s^{2}; Moon

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9.8 m/s^{2}; Earth

25 times; Increase

Gravitational force,
In order to notice the gravitational force of attraction between any two objects, at least one of the objects on the earth should have an extremely large mass. Since no object on the earth has an extremely large mass, we cannot notice such forces ; The two objects in a room do not move towards each other because they have small masses, so the gravitational force of attraction between them is very, very weak.

19.6 m/s^{2}

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Elliptical; That the orbit of a planet around the sun is ‘circular’

9.23 m/s^{2}, 7.34 m/s^{2}, 3.08 m/s^{2}, 1.49 m/s^{2}, 0.57 m/s^{2}, 0.30 m/s^{2}

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Kg/m^{3}

1 Kg/m^{3}

Pressure

Pascal or n/m^{2}

Upward direction