Inner part of a cupboard is in the cuboidical shape with its length, breadth and height in the ratio `1: sqrt2: 1`. What is the angle made by the longest stick which can be inserted cupboard with its base inside.

One magnet is cut perpendicular to its axis and divided into two pieces with the lengths in the ratio 2 : 1. Then ratio of their pole strength is ......

The capacity of a cuboidal water tank is 1,00,000 litres. If its length is 5 m and breadth is 4 m, find its height.

In a cuboid, the area of the face with sides length and breadth is 120 cm^(2) . If the height of the cuboid is 5 cm, then its volume is ……… cm^(3) .

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find its length and breadth.

The outer measurements of a cuboidal tank are length 5 m, breadth 4 m and height 2 m. Square tiles of length 20 cm are to be fixed on its outer surfaces except the base. Find the number of tiles required. Find the cost of tiles if a box of 10 tiles costs Rs. 250.

A rectangular park is to be designed whose breadth is 3m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12m (see the given figure). Find its legth and breadth.

A thin circular wire of radius R rotatites about its vertical diameter with an angular frequency omega . Show that a small bead on the wire remain at its lowermost point for omegalesqrt(g//R) . What is angle made by the radius vector joining the centre to the bead with the vertical downward direction for omega=sqrt(2g//R) ? Neglect friction.

A rain drop of radius 2 mm falls from a height of 500 m above the ground .It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height , it attains its maximum (terminal) speed, and moves with uniform speed thereafter .What is the work done by the gravitational force on the drop in the first and second half of its journey ?What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 1 ms^(-1) ?

A rain drop of radius 2mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its speed on reaching the ground is 10 ms^(-1) ?

A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2 : 1 . What will be the ratio of their nuclear size (nuclear radius)?