Let us assume that our galaxy consists of `2.5 xx 10^11` stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be `10^5` ly.

Two stars each of one solar mass (= 2xxl0^30 kg) are approaching each other for a head on collision. When they are a distance 10^9 km , their speeds are negligible. What is the speed with which they collide ? The radius of each star is 10^4 km . Assume the stars to remain undistorted until they collide. (Use the known value of G).

A magnet makes 40 oscillations per minute at a place having magnetic field intensity of 0.1xx10^(-5)T . At another place, it takes 2.5 sec to complete one vibrating. The value of earth's horizontal field at that place is

Two small spheres each of mass 10^6kg are suspended from a point by silk threads 50 cm long. These are equally charged and repel each other to a distance of 20 cm apart. Calculate the charge on each sphere. Take g = 10 ms^-2

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?

A radioactive source, in the form of a metallic sphere of radius 10^(-2)m emits beta -particles at the rate of 5xx10^(10) particles per second. The source is electrically insulated. How long will it take for its potential to be raised by 2V, assuming that 40% of the emitted beta -particles escape the source.

One day in the morning, Ramesh filled up 1/3 bucket of hot water from geyser, to take bath. Remaining 2.3 was to be filled by cold water (at room temperature) to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend to something which would take some time say 5 - 10 minutes before he could take bath. Now the he had two options: (i) fill the remaining bucket completely by cold water and then attend to the work, (ii) first attend to the work and fill the remaining bucket just before taking bath. Which option do you think would have kept water warmer ? Explain.

A mathematics paper consists of 10 questions divided into two parts I and II, each part containing 5 questions. A student is required to attempt 4 questions in all, taking at least 2 questions from each part. In how many ways can the student select the questions ?

A copper atom consists of copper nucleus surrounded by 29 electrons. The atomic weight of copper is 63.5mol e^(-1) . Let us now take two pieces of copper each weighing 10g. Let us trandfer one elcetron from one piece to another for every 100 atoms in that piece. What will be the Coulomb force between the two pieces after the trandfer of electrons, if they are 1cm apart? Avogadro number= 6xx10^(23) mol e^(-1) , charge on an electron =- 1.6xx10^(-19)C.

The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 xx 10^28 m^-3 . How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 xx 10^-6 m^2 and it is carrying a current of 3.0 A.