A small terrace at a football ground comprises of 15step each of which is 50m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (see fig.) Calculate the total volume of concrete required to build the terrace.
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A copper wire of resistivity 1.6xx10^-8 ohm-m has a cross sectional area of 20xx10^-4 cm^2 . Calculate the length of wire required to make a 10 ohm coil.

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m^2 , what will be the cost of painting all these cones (use pi = 3.14 , and take sqrt(1.04)=1.02 ) ?

A conductivity cell has its electrodes 1 cm apart and each electrode has area of cross-section 2 cm^(2) , when filled with M/50 solution of sodium acetate, the cell shows a resistance of 166.5 ohms. Calculate the molar conductance of sodium acetate solution at the givne concentration.

The pillars of a temple are cylindrically shaped (see Fig. 13.26). If each pillar has a circular base of radius 20 cm and height 10 m, how much concrete mixture would be required to build 14 such pillars?

Concentrated aqueous sulphuric acid is 98% H_2SO_4 by mass and has a density of 1.80gmL^-1 . Volume of acid required to make one litre of 0.1 M H_2SO_4 is

A small sphere rolls down without slipping from the top of a track in a vertical plane. The track has an elevated section and a horizontal part is 1.0 m above the ground level and the top of the track is 2.4 m above the ground. Find the distance on the ground with respect to the point B (which is vertically ) below the end of the track as shown in figure. Where the sphere lands. During its flight as a projectile does the sphere continue to rotate about its centre of mass? Explain.

A magnetic field of 100 G (1 G = 10^-4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10^-3 m^2 . The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^-1 . Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

Five square flower beds each of sides 1.2 m are dug on a piece of land 4.8m long and 4.2 m wide.What is the area of the remaining part of land?

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m^2 is Rs 4.