Advertisements
Advertisements
प्रश्न
How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 108 km.
Advertisements
उत्तर १
Orbital radius of the Earth around the Sun, r = 1.5 × 1011 m
Time taken by the Earth to complete one revolution around the Sun,
T = 1 year = 365.25 days
= 365.25 × 24 × 60 × 60 s
Universal gravitational constant, G = 6.67 × 10–11 Nm2 kg–2
Thus, mass of the Sun can be calculated using the relation,
`M = (4pi^2r^3)/(GT^2)`
= `(4xx(3.14)^2 xx (1.5xx10^11)^3)/(6.67xx10^(11)xx(365.25xx24xx60xx60))^2`
=`(133.24xx10)/(6.64xx10^(4)) = 2.0xx10^(30)` kg
Hence, the mass of the Sun is 2 × 1030 kg.
उत्तर २
The mean orbital radius of the Earth around the Sun
R = 1.5 x 108 km = 1.5 x 1011 m
Time period, T = 365.25 x 24 x 60 x 60 s
Let the mass of the Sun be M and that of Earth be m.
According to law of gravitation
`F= G(Mm)/RA^2` ...(i)
Centripetal force
`F = (mv^2)/R = m.R.omega^2` ...(ii)
`(GMm)/R^2 = m.R.omega^2`
=`(mR.4pi^2)/T^2`
`:. M = (4pi^2R^3)/(G.T^2)` [∵ `omega = (2pi)/T`]
= `(4xx(3.14)^2xx(1.5xx10^11)^3)/(6.67xx10^(-11)xx(365.25 xx 24 xx 60xx60)^2)`
= `2.009 xx 10^(30) kg = 2.0 xx 10^(30) kg`
संबंधित प्रश्न
Answer the following:
An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) (i) a, (ii) b, (iii) c, (iv) 0.
State the universal law of gravitation. Name the scientist who gave this law.
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 ?
Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?
Suppose the gravitational potential due to a small system is k/r2 at a distance r from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?
The weight of an object is more at the poles than at the equator. Is it beneficial to purchase goods at equator and sell them at the pole? Does it matter whether a spring balance is used or an equal-beam balance is used?
Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
Two spherical balls of mass 10 kg each are placed 10 cm apart. Find the gravitational force of attraction between them.
Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two.
A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.
Where will you weigh more: at the moon's surface or at the earth's surface?
A force can produce ________, In an object at rest. It can __________ an object and change its __________ of motion.
Explain why:
The atmosphere does not escape.
Answer the following question.
State Newton’s law of gravitation and express it in vector form.
State the universal law of gravitation and derive its mathematical expression.
For the weight of body of mass 5 kg to be zero on equator of the earth, angular velocity of the earth must be (The radius of earth = 6400 km, acceleration due to gravity = 10 m/s2).
Law of gravitation gives the gravitational force between
Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is
The acceleration of the Moon towards the Earth is approximately:
