A wire attached to a vertical pole of height 18m is 24m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

A wire suspended vertically from one of its end is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1mm. Find the elastic energy in the wire.

You want to erect a pole of height 10 m with the support of three ropes. Each rope has to make an angle 30^(@) with the pole. What should be the length of the rope?

A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

A unifrom rope of length L and mass m_1 hangs vertically from a rigid support.A block of mass m_2 is attached to the free end of the rope.A transverse pulse of wavelengh lambda_1 is produced at the lower end of the rope.The wavelength of the pulse when it reaches the top of the rope is lambda_2 .The ratio lambda_1//lambda_2 is :

A metre stick weighing 240 g is pivoted at its upper end in such a way that it can freely rotate in a vertical plane through this end figure. A particle of mass 100 g is attached to the upper end of the stick through a light sting of length 1 m. Initially the rod is kept veritcal and the string horizontal when the system is released from rest. The particle colides with the lower end of the stick and sticks there. Find the maximum angle through which the stick will rise.

The image of man height 1.8m , is of length 1.5 cm on the film of a camera . If the film is 3 cm from the camera, how far is the man from the camera ?

The pulley shown in figure has a radius of 20 cm and moment of inertial 0.2 kg-m^2. The string going over it is attached at one end to a vertical sprign of spring constant 50 N/m fixed from below and supports a 1 kg mas at other end. The system is released from rest with the spring at its natural length. Find the speed of the block when it has desceds through 10 cm. Take g=10 m/s^2 .

Figure shows a light rod of length l rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the rod in a horizontal position. There is a fixed smooth ring at a depth h below the initial position of the hook and the hook gets into the ring as it reaches there. What should be the minimum value of h so that the block moves in a complete circle about the ring?

Two vertical poles of heights, 20 m and 80 m stand 50m apart on a horizontal plane. The height (in m) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is

A vertical pole of a length 6 m casts a shadow of 4 m long on the ground . At the same time a tower casts a shadow 28 m long . Find the height of the tower.