The length of the shadow of a pole inclined at `10^@` to the vertical towards the sun is 2.05 metres, when the elevation of the sun is `38^@`. The length of the pole is

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60^@ . He moves away from the pole along the line BC to a point D such that CD =7m. From D, the angle of elevation of the point A is 45^@ . Then the length of the pole is:

Two identical magnetic with a length 10 cm and weight 50 g of each are arranged freely with their like poles facing in a inverted vertical glass tube. The upper magnet hangs in the air above the lower one so that the distance between the nearest pole of the magnet is 3mm. Pole strength of the poles of each magnet will be

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev//s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm^2 . Calculate the elongation of the wire when the mass is at the lowest point of its path.

Find the rate of change of area of a square when its side is increasing at the rate of 2 cm/min and the length of the side is 10 cm.

A steel wire of mass mu per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains < < longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m^-3 (Young's modulues Y = 2 xx 10^11 N m^-2)

A short bar magnet of magnetic movement 5.25 xx 10^-2 J T^1 is placed with its axis perpendicular to the earth’s field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45^@ with earth’s field on its axis. Magnitude of the earth’s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.

On a horizontal plane there is a vertical tower with a flag on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60^@ and 30^@ respectively. Find the height of the tower and flag pole mounted on it.

A large magnet is broken into two pieces, so that their lengths are in the ratio 2:1. The pole strengths of the two piece will be

A steel tape 1 metre long is correctly calibrated for temperature of 27.0^@C . The length of a steel rod measured by this tape is found to be 63.0 cm on a h ot day when the temperature is 45^@C . What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0^@C ? Coefficient of linear expansion of steel = 1.20 xx 10^-5 C^-1 .

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) ) .