Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is `4.22 xx 10^8 m`. Show that the mass of Jupiter is about one-thousandth that of the sun.

How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 xx 10^8 km .

The principle of 'parallax' is used in the determination of distance of nearby stars. The role of distant object O there is now taken by nearby distant stars. The baseline AB is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is the baseline is about the disameter of the earth's orbit = 3 xx 10^11 m. However, even the nearest stars are so distant that with such a long baseline theyshow parallax only of the order 1 s of arc or so. A parsec is a convenient unit of length on the astronomical sxale. It is the distance of an object that will show a parallar of 1s of arc from opposite ends of a baseline equal to the distance from the Earth to the Sum How much is a parsec in terms of metre?

Earth also moves in circular orbit around the sun once every year with an orbital radius of 1.5xx10^(11)m . What is the accerelation of the earth ( or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m//s^(2) ?

A planet is revolving round the sun in elliptical orbit. The maximum and minimum distances of the planet from the sun are 2 xx 10^2 m and 2 xx 10^10 m respectively. The speed of the planet when it is nearest to sun is 2 xx 10^15 ms^-1 What is the speed when it is farthest to the sun?

Calculate the mass of the earth. Given radius of the earth =6.4xx10^-6 m and g = 9.8 m//s^2

Calculate the frequency of rtevolution of electron in the first Bohr orbit of hydrogen atom,if the radius of the first Bohr orbit is 0.5 overset @A and the velocity of electron in the first orbit is 2.24 xx 10^6 m s^(-1) .

A current I=3.36 (1+2t)xx 10^-2 A increases at a steady rate in a long straight wire. A small circular loop of radius 10^-3 m has its plane parallel to the wire and is at a placed at a distance of 1 m from the wire. The resistance of the loop is 8.4 xx 10^-4 Omega . find the megnitude and the direction of the induced current in the loop.

The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^-1 , what is the speed of ejection of the liquid through the holes ?

The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of water. Hie water pressure at the bottom of the trench is about 1.1 xx 10^8 Pa. A steel ball of initial volume 0.32 m^3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?