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).

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s^-1 collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?

Two small spheres each of mass 10 mg are suspended from a poimt by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.28 m. If g = 10 ms^-2 , what is the charge on each ?

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

Two pith-balls each of mass 5xx10^-4 kg are suspended from the same point by silk threads 0.2 m long equal charges are given to the balls, which separate, until the threads enclose an angle of 30^@ , Calculate the charge on each pith-ball.

Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.)

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.

A bird is tossing (flying to and fro 0 between two cars moving towards each other on a straight road. On car has a speed of 18 km /h while the other has the speed of 27 km /h. The bird starts moving from first caer towards the other and is moving with the speed of 36 km /h and when the two cars were separated by 36 km. What is the total distance comered by the bird ? What is the total displacement of the bird ?

A trolley of mass 200 kg moves with a uniform speed of 36 km//h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^-1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley ? How much has the trolley moved from the time the child begins to run ?