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.

Ratio of length, breadth and height are in the ratio 5:2:1. Its volume is 1250 cm^3 . Find its dimensions.

A capillary tube of radius 1 mm is kept vertical with the lower end in water. (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part (a), find the angle theta made by the water surface in the capillary with the wall.

Two cylindrical rods of same length have the area of cross section in the ratio 2:1 rods are made up of same material, which of them conduct heat faster ?

The lower end of a capillary tube of radius 1 mm is dipped vertically into mercury. (a) Find the depression of mercury column in the capillary. (b) If the length dipped inside is half the answer of part (a), find the angle made by the mercury surface at the end of the capillary with the vertical. Surface tension of mercury =0.465Nm^-1 and the contact angle of mercury with glass =135^@ .

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.

A 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2 A. a. What is the field at the centre of the coil ? b. What is the magnetic moment of this coil ? The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. A unifrom magnetic field of 2 T in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of 90^@ under the influence of the magnetic field . c. What are the magnitudes of the torques on the coil in the initial and final position ? d. What is the angular speed acqired by the coil when it has rotated by 90^(@) ? The moment of inertia of the coil is 0.1 kg m^2

If the ratio of the height of a tower and the length of its shadow is sqrt(3):1 , then the angle of elevation of the sum had measure.

A long solenoid with 20 turns per has a small loop of area 2Cm2 placed inside the solenoid normal to its axis. If the circuit carried by the solenorid changes steaditly from 1Ato 3A in 0.2s. What is the induced emf in the loop while the current ins charging.

a.Figure shows a cross-section of a 'light pipe' made of glass fibre of refractive index 1.68 The outer converting of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections insides the pipe take place as shown in the figure. b.What is the answer if there is no outer converting of the pipe ?