Select Board & Class
what is the difference between density and relative density ?
WHEN A PLANET MOVES AROUND THE SUN, ITS
(A) AREAL VELOCITY IS CONSTANT
(B) LINEAR VELOCITY IS CONSTANT
(C) ANGULAR VELOCITY IS CONSTANT
(D) ALL THE VELOCITIES ARE CONSTANT
How does a lactometer work ?
Why Newton's law of gravitation called universal law
what are the importance of universal law of gravitation??
List two factors on which buoyant force depends.
A sharp knife is more effective than a blunt knife.why?
what happens to the gravitational force between two objects if
i) the mass of one object is doubled
ii) distance between two objects is doubled
iii) masses of both the objects are doubled
what is the difference between density and relative density of a substance
The picture that opens this lesson shows our location in the Milky Way galaxy. We are about 26,000 light years away from the centre of the galaxy. We are residing in this location from the very beginning of the Universe. This shows that there exists a powerful force that holds us in our place since the inception of the Universe. This force binds everything from stars togalaxiestosuperclustersand is known as theGravitational force.
It is common to see things falling to the ground. The falling of a body to the ground is attributed to Earths attraction for it. In fact, the weight of a body is expressed in terms of this force of attraction.
Newtons experiments showed that Earths attraction, when at a constant distance from another body, varied directly with the mass of the other body. However, this was only a partial expression of the general law of gravitation. This law states thatevery particle of matter 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 them.
All planets in the solar system are bound to revolve in their fixed orbits by the gravitational attraction of the sun. The same force of gravity acts between Earth and the moon, making the moon revolve around Earth in its fixed orbit.
Let two objectsIandII,of massesM1andM2respectively, be placed at a distancedfrom each other. As per the law of gravitation, the following two assertions can be made about the force of gravity (F) between the two objects.
(a)The force of gravity between the two objects is directly proportional to the product of their masses. This is expressed as:
F∝M1×M2(By Product rule)
(b)The force of gravity between the two objects is inversely proportional to the square of the distance between them. This is expressed as:
F∝ (1/d2)(By Inverse-Square rule)
On combining both the equations, we obtain:
F ∝M1M2d2 or F =GM1M2d2 " width="195" height="31" src="http://img1.mnimgs.com/img/study_content/editlive_lp/62/2013_02_09_10_27_23/mathmlequation3568840687176322813_1624553838655146822.png" /
Where, G is a constant calledUniversal Gravitational ConstantorNewtons constant.
Universal Gravitational Constant (G) is a constant of proportionality. Its value is constant at all places in the universe. Its value does not depend on the medium between two bodies.
SI unit of G
The force of gravity (F)between two objects of massesM1andM2,which are at a distancedfrom each other, is given as:
F = GM1M2d2 or G =Fd2M1M2 " src="http://img1.mnimgs.com/img/study_content/editlive_lp/62/2013_02_09_10_27_23/mathmlequation6404826584263522868.png" /
On substituting the SI units of the various quantities in this equation, we obtain: G = Nm2/ kg2
Therefore, the SI unit of G is Nm2/kg2.
Value of G
Henry Cavendish found the value ofUniversal Gravitational Constant,G with the help of a very sensitive balance. Its value is6.673 × 1011Nm2/kg2
Consider two bodies, each having the mass 1 kg. They are placed at a distance 1m from each other. Using the value of G, the force of attraction is given as:
CAN U SIMPLIFY THIS EXPRESSION
The value of universal gravitational constant (G) was first determined by Henry Cavendish through the torsion bar experiment. The apparatus of this experiment comprises two pairs of spheres. Each pair of spheres forms a dumbbell having a common axis, as shown in the figure. One of the dumbbells is suspended from a quartz fibre. It rotates freely when the fibre is twisted. The position of a reflected light spot from a mirror attached to the fibre gives the measure of the amount of twists. The second dumbbell can be swivelled in such a way that each of its spheres is close to one of the spheres of the other dumbbell. The gravitational attraction between the two pairs of spheres twists the fibre and the magnitude of the force of gravity is calculated by measuring the amount of twists in the fibre.
The value of G, as determined by Cavendish, came out to be6.67 × 10-11Nm2/kg2.
The universal law of gravitation helps us understand several natural phenomena. Some of these are given below.
Dropped objects fall toward the ground.
Earth pulls all objects toward itself through the gravitational force. Hence, when any object is dropped, it falls toward the ground.
The moon revolves around Earth.
The moon is attracted by Earths gravitational force. This keeps the moon revolving around Earth in its orbit of movement.
The planets revolve around the sun.
The gravitational attraction between the sun and the planets binds the planets in their respective orbits around the sun.
High and low tides occur on Earths surface.
The water present on Earths surface (in oceans, seas, etc.) is attracted by the gravitational forces of the sun and moon. Hence, the level of water in the seas and oceans rises and falls depending on the relative positions of the sun and moon. This causes high and low tides on Earth.
A German astronomer Kepler concluded the orbits of the planets to be circular. the laws which he gave are:
First Law: The orbits of the planets are in the shape ofellipse, having the sun at one focus.
In the figure, the sun is not at the centre of the ellipse. It is at one of the foci marked X. The planet follows the ellipse in its orbit. This means that the distance between a planet and the sun constantly changes as the planet revolves in its orbit.
Second Law: The area swept over per hour by the radius joining the sun and the planet is the same in all parts of the planets orbit.
In the figure, the imaginary line joining the sun and the planet sweeps out equal areas in equal times. The planet moves faster when it is nearer to the sun. Thus, a planet executes elliptical motion with constantly changing speed as it moves around the sun in its orbit. The point of nearest approach of the planet to the sun is termed perihelion and the point of greatest separation is termed aphelion.
Third Law: The squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun.
It implies that the time taken by a planet to revolve around the sun increases rapidly with the increase in the radius of its orbit.
Newtons universal law of gravitation states that the force between two bodies is inversely proportional to the square of the distance between them. Hence, this law is also known as the inverse-square rule. Mathematically, this can be expressed as:
Newton used Keplers third law of planetary motion to arrive at the inverse-square rule. He assumed that the orbits of the planets around the sun are circular, and not elliptical, and so derived the inverse-square rule for gravitational force using the formula forcentripetal force. This is given as:
F=mv2/r2...(2) where,mis the mass of the particle,ris the radius of the circular path of the particle andvis the velocity of the particle.
Newton used this formula to determine the force acting on a planet revolving around the sun. Since the massmof a planet is constant, equation (2) can be written as:
Now, if the planet takes timeTto complete one revolution around the sun, then its velocityvis given as:
v= 2r/T...(4) where,ris the radius of the circular orbit of the planet
or,v∝r/T...(5) [as the factor 2 is a constant]
On squaring both sides of this equation, we get:
On multiplying and dividing the right-hand side of this relation byr, we get:
v2 ∝r2T2 ×rr or v2 ∝r3T2×1r ...(7) " src="http://img1.mnimgs.com/img/study_content/editlive_lp/62/2013_02_09_10_27_23/mathmlequation8727827952146380765.png" /
According to Keplers third law of planetary motion, the factor r3/ T2is a constant. Hence, equation (7) becomes:
On using equation (8) in equation (7), we get:
F ∝ 1r ×1r or F ∝1r2 " /
Hence, the gravitational force between the sun and a planet is inversely proportional to the square of the distance between them.
An imaginary planetP, with an orbit of radiusR, completes one revolution around a star in 64 days. Another planetQhas an orbit of radius 4R. How much time will it take to complete one revolution around the same star?
According to Keplers third law of planetary motion:
Where,is the time period of revolution ofis the radius of the orbit ofP
Where,is the time period of revolution ofQandis the radius of the orbit ofQ
On dividing (1) by (2), we get:
Why do objects float or sink when placed on the surface of liquid?
the density of ice is 0.9 g/cm3. When it floats in water, what fraction of its volume will remain above surface?
what is the relationship between "G" and "g"?
Difference between thrust and pressure?
thrown up vertically returns to the thrower after 6 s. Find
velocity with which it was thrown up,
maximum height it reaches, and
position after 4 s.
A solid weighs 80g in air and 64g in water. Calculate its relative density. Also tell, when kept in water would the object float or sink.
happens to the force between two objects, if
mass of one object is doubled?
distance between the objects is doubled and tripled?
masses of both objects are doubled?
Guys, it's urgent, plz answer them immediately...
Q1. A block weighing 1.0 kg is in the shape of a cube of length 10 cm. It is kept on a horizontal table. Find the pressure on the portion of the table where the block is kept. (ans. 1000Pa)
why a truck or a motorbus has wider tyres
An object is dropped from rest at a height of 150 m and simultaneously
another object is dropped from rest at a height 100 m. What is the difference
in their heights after 2 s if both the objects drop with same accelerations?
How does the difference in heights vary with time?
The period of revolution of a certain planet in an orbit of radius R is T. Its period of revolution in an orbit of radius 4R will be?
what are the characteristics of gravitational force.......????
relative density of gold is 19.3.if the density of water is 1000kg/m3 ,what is density of gold in si unit?
radius of an iron sphere is 0.21 cm If density of iron is 7.80g/cc calculate mass
why do we use constant e.g. K, G etc., to remove proportional sign from the equations?
starting from Newton's law of gravitation show that the value of "g" decreases as one goes above the earth's surface.
difference between mass and weight
. Rajeev went from Delhi to Chandigarh on his motorbike. The odometer of the bike read
WHAT IS THE S.I. UNIT OF UPTHRUST?
Write the S.I. unit of G. Why is gravitational constant (G) known as universal constant ?
what is the difference between thrust and force?
the acceleration due to gravity on a planet is 1.96m/s2 .If it is safe to jump from a height of 3m on the earth, the corresponding height of the planet will be ?
Determine the height h above the surface where the value of g
i=Falls to 1% of the value at the surface
ii-falls by 1% of the value at the surface
B-Sir/mam i was getting confused with the variation in "g" so i ll the statements could yu check
How archimedes principle is used to determine the purity of gold?
A test tube is loaded with lead shots so that it floats in a liquid immersed to a mark on the tube. The total weigh of tube and lead shots is 30 gf. the tube is then placed in water and lead shots are added to sink the tube to the same mark. Now, the tube and lead shots weigh 35 gf. Calculate the relative density of liquid.
a stone is allowed to fall from the top of a tower 100m high and at the same time another stone is projected vertically upwards frome the ground with a velocity of 25ms-1 . calculate when and where the 2 stones will meet.
When an object is immersed into the fluid two forces act on the object in the vertically opposite directions. Name them and also write the factors on which the magnitude of these forces depends on.
If th relative density of a substance is greater than 1. What does it signify?
A body weighs 63 N on the surface of the earth. What is the gravitational force exerted on it due to the earth at a height equal to half the radius of the earth?
the weight of a body on the surface of earth is 392n.what is the mass when g=9.8m/s.if the body is taken to moon, it weighs 64n.what is the mass of a body on the moon?calculate the gravity on moon?
Name two substances whose density cannot be measured.
1) State Archimedes principle?
2) Give two applications of archimedes principle.
a student lifts an object in the upward direction.in doing so he applies force on the object in the upward direction and displaces it in that direction.(however , the force of gravity is also acting on the object?
A solid weighs 80g in air, 68g in water and 60g in oil. Calculate the relative density of oil and solid.
difference between g and G .
how is the least count and the zero error of the spring balance is calculated?
name the factors affecting pressure
State the laws of floatation.
prove that if a body is thrown vertically upwards, the time of ascent is equal to the time of decent.
Q1 Give reasons:
A solid sphere has a radius of 1.5 cm and a mass of 0.038 kg. What is the relative density of the sphere?
Define one pascal.
1. Explain why a balloon filled with helium gas rises in air. Why does the balloon rise to a particular height above ground and does not rise further ?
At what height above the earth's surface would the value of acceleration due to gravity be half of what it is on the surface? Calculate.
A piece of iron of density 7.8 * 103kg/m3 and volume 100 cm3 is totally immersed in water. Calculate
(a) The weight of the iron piece in air
(b) The upthrust
(c) Apparent weight in water
A stone is thrown vertically upward with a velocity 40m/s and is caught back. Taking g=10m/s2.calculate the maximum height reached by the stone
A wooden cube first float inside the water whena 100g mass is placed on it.When the mass is removed,the cube is 1cm above the waterlevel.The side of cube is
(a)10cm (b)15cm (c)5cm(d)20cm
what are the applications of archimedes principle???
State universal law of gravitation.The gravitational force between two objects is 100N.How should the distance between the objects be changed so that the force between them becomes 50N.
write the factor on which pressure depends
(3) 3.01 * 105 Pa (4) 4.01 * 105 Pa
RELATIONSHIP BETWEEN SMALL g AND CAPITAL G
how to make model of lactometer on archimedes principle
why does buildings have wide foundations?
prove that if a body is thrown vertically upward , the time of ascent is equal to the time of descent.
If same force acts on a body, what will happen ton acceleration of the object when its (a) mass is doubled (b) Mass is made 1/4th? Also determine the ratio of acceleration in the above two cases.
A sphere of mass 40 kg is attraced by a second sphere of mass 15 kg when their centers are 20 cm apart, with a force of 0.1 milligram weight. Calculate the value of gravitational constant.
loaded test tube placed in pure milk sinks to a certain mark (M). Now some water is mixed with the milk. Will the test tube sink more or less? Explain.
A Piece of ice is placed gently on the surface of water in a glass so that when ice floats, the water comes up to the brim of the glass. what will happen to the level of water when the ice melts? will it overflow? (2) in the above case what will happen if instead of water the glass is filled with (a) with a liquid denser than water. (b) a liquid lighter than water.
Copyright © 2021 Aakash EduTech Pvt. Ltd. All rights reserved.
E.g: 9876543210, 01112345678
We will give you a call shortly, Thank You
Office hours: 9:00 am to 9:00 pm IST (7 days a week)