Two small spheres each having mass m kg and charge q coulomb are suspended from a point by insultaing threads each l metre long but of negligible mass. If `theta` is the angle, each string makes with the vertical when equilibrium has been attained show that `q^2 = (4m g l^2 sin ^2 theta tan theta) 4 pi upsilon_0`

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.

Two pith-balls each weighing 10^-3 kg are suspended from the same point by mans of silk threads 0.5 m long. On charging the pith-balls equally, they are found to repel each other to a distance of 0.2 m. Calculate the charge on each ball?

If a small sphere of mass m and charge q hangs from a silk thread at angle theta with a charged coducting plate, show that the equilibrium of the sphere, the surface charge density for the plate is epsilon_0 = (mg)/q tan theta

The stone of mass 100 g is suspended from the end of a weightless string of length 100 cm and is allowed to swing in a vertical plane.The speed of the mass is 2 m s^-1 when the string makes an angle of 60^@ with the vertical .Calculate the tension in the string at theta = 60^@ .Also,caculate the speed of the stone when it is in the lowest poition. (g=9.8 m s^(-2) ) .

A small ball of mass 2 xx 10^-3 kg, having a charge 1 mu C, is suspended by a string of length 0.8 m. Another identical ball having the same charge is kept at the point of suspension. Determine the minimum horizontal velocity that should be imparted to the lower ball so that it can make a complete revolution.

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).

As shown in the given figure. the two sides of a step ladder BA and CA are 1.6 m long and hinged at A.A rope DE, 0.5 m is tied half way up. A weight 40 kg is suspended from a point F, 1,2 m from B along the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in te rope and forces exerted by the floor on the ladder. (Take g = 9.8 ms^-2 ) (Hint: consider the equilibrium of each side of the ladder separately).