A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of m `1/4` and a tread of `1/2` m (see the given figure). Calculate the total volume of concrete required to build the terrace.

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid bricks. Each step has a rise of 1/4 m and a tread of 1/2 m. Calculate the total volume of the terrace. [Hint: Volume of the first step =1/4 xx 1/2 xx 50 m^(3) ]

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see the given figure). Find how much he would spend for the tiles, if the cost of the tiles is Rs. 360 per dozen.

An electrician has to repair an electric fault on a pole of height 5m. She needs to reach a point 1.3m below the top of the pole to undertake the repair work (see the given figure). What should be the length of the ladder that she should use which, when inclined at an angle of 60^(@) to teh horizontal, would enable her to reach the required position? Also, how far from the foot of the pole shoudl she place the foot of the ladder? (you may take sqrt3= 1.73 )

A 1.2m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60^(@) . After some time, the angle of elevation reduces to 30^(@) (see the given figure). FInd the distance travelled by the balloon during the interval.

Three blocks of m asses 1 kg, 2 kg and 3 kg are placed in contact w ith each other on a horizontal frictionless surface, as show n in figure. A force of 12 N is applied as shown in the figure. Calculate (i) the acceleration of the system o f these three blocks, (ii) the contact force acting on 2 kg block by first block of 1 kg and (iii) the contact force on 3 kg block.

A man travels a distance of 1.5 m towards East, then 2.0 m towards South and finally 4.5 m towards north. (i) Calculate the total distance travelled. (ii) Calculate the resultant displacement.

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.