A piece of wire 8 m. in length is cut into two pieces, and each piece is bent into a square. Where should the cut in the wire be made if the sum of the areas of these squares is to be `2m^(2)`?

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 spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of:

A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60^(@) at its centre. Find the radius of the circle.

A wire of length I is cut into three pleces. What Is the probability that the three pieces form a triangle ?

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

If the spring is cut in two equal piece the spring constant of every piece decreases.

(a) What happens if a bar magnet is cut into two pieces: (i) transverse to its length, (ii) along its length ?

A steel wire has a length of 12.0m and a mass of 2.10kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20^(@)C= 343ms^(-1)

Sum of the areas of two squares is 468m^(2) . If the difference of their perimeter is 24m , find the sides of the two squares.