A non-uniform bar of weight W is suspended at rest by two strings of negligible weight as shown in Fig.7.39. The angles made by the strings with the vertical are `36.9^@` and `53.1^@` respectively. The bar is 2 m long. Calculate the distance d of the centre of gravity of the bar from its left end.

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

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig. 9.15. The cross-sectional areas of wires A and B are 1.0 mm^2 and 2.0 mm^2 , respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses :

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig. 9.15. The cross-sectional areas of wires A and B are 1.0 mm^2 and 2.0 mm^2 , respectively. At what point along the rod should a mass m be suspended in order to produce equal strains in both steel and aluminium wires.:

A bar magnet is 0.1 m long and its pole strength is 12 Am. Find the magnetic induction at a point on its axis at a distance of 0.2 m from its centre.

A bar magnet of length 0.1 m has a pole strength of 50 A m. Calculate the magnetic field at distance of 0.2 m from tis centre on its axial line

A bar magnet of length 0.1 m has a pole strength of 50 A m. Calculate the magnetic field at distance of 0.2 m from tis centre on its equitorial line.

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 metal bar AB can slide on two parallel thick metallic rails separated by a distance l. A resistance R and an inductance L are connected to the rails as shown in the figure. A long straight wire carrying a constant current I_(0) is placed in the plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance x_(0) from the long wire. At t=0, it is made to slide on the rails away from wire. Answer the following questions. Find a relation among i, (di)/(dt) and (d phi)/(dt) , where i is the current in the circuit and phi is the flux of the megnetic field due to the long wire through the circuit.