A road bridge over an irrigation canal have two semi circular vents each with a span of 20 m and the supporting pillars of width 2m. Use figure to write the equations that represent the semi verticular vents.

Figure shows two block A and B , each having a mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block A can slide is smooth. The block A is attached to spring constant 40 N//m whose other end is fixed to a support 40 cm above the horizontal surface. Initially, the spring is vertical and unstretched when the system is released to move. Find the velocity of the block A at the instant it breaks off the surface below it. Take g = 10 m//s^(2) .

Two short bar magnets have magnetic moments 1.20 Am^(2) and 1.00 Am^(2) respectively . They are kept on a horizontal table parallel to each other with their north poles pointing towards the south . They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction the mid point O of the line joining their centers is (Horizontal components of Earth's magnetic induction is (3 xx 10^(-5) Wb m^(-2) ) ...............

Two short bar magnets of length 1cm have magnetic moments 1.20 " Am"^(2) and 1.00 " Am"^(2) , respectively . They are kept on a horizontal table parallel to each other with their North poles pointing towards the south . They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the midpoint O of the line joining their centers is ( Horizontal components of Earth's magnetic induction is 3.6 xx 10^(-5) Wb m^(-2) ).

A track consists of two circular pars ABC and CDE of equal radius 100 m and joined smoothly as shown in figure.Each part subtends a right angle at its centre. A cycle weighing 100 kg together with rider travels at a constant speed of 18 km/h on the track. A. Find the normal contact force by the road on the cycle when it is at B and at D. b.Find the force of friction exerted by the track on the tyres when the cycle is at B,C and D. c. Find the normal force between the road and the cycle just before and just after the cycle crosses C. d. What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take g=10 m/s^2