The sides of a triangular field aré `35 m`, `42 m` and `47 m`, There is a wall around the field, and within it, at each corner a cow is tied with a piece of rope `7 m` Iong. What is the total area of the region that the three cows can graze?

Two fences are made in a grass field as shown in the figure . A cow is tied at the point O with a rope of length 3m. If there is no fences find the maximum area of grass that cow can graze.

A solenoid is 2.0m long and 4.5 cm in diameter. It has five layers winding each of 900 turns each and carries a current of 7.5 A. what is magnetic field at the centre of the solenoid?

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 15A 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 ferromagentic.

Two large, thin metal plates are parallel and close io each other. On their inner faces, the plates have surface charge densities of opposite signs and of mag nitude 17.0 xx 10^-22 C//m^2 . What Is E (Electric field):-In the outer region of the first plate, and in the outer region of the second plate.

A man owns a field of area 1,000 sq.m. He wants to plant fruit trees in it. He has a sum of Rs. 1,400 to purchase young trees. He has the choice of two types of the tree. Type A requires 10 sq.m of ground per tree and cost. Rs. 20 per tree and type B requires 20 sq.m of ground per tree and cost Rs. 25 per tree. When fully grown, type A produces an average of 20 kg fruit Which can be sold at a profit of Rs. 2 per kg and type B produces. an average of 40 kg of fruit which can be sold at a profit.of Rs. 1.50 per kg. How many of each type should he plant to achieve maximum profit when the trees are fully grown? What is the maximum profit?

A closely wound solenoid of 2000 turns and area of cross-section 1.6x10-^4 m^2 , carrying a current of 4.0A, is suspended through its centre allowing it to turn in a horizontal plane. Br What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5x10^2 is set up at an angle of 30° with the axis of the solenoid?

Consider all rectangles that can be made with a 1m long rope. Take one of its side as x cm and the area enclosed as a(x) sq.cm. i) Write the relation between a(x) and xas in equation ii) Why are the numbers a(10) and a(40) equal? iii) To get the same number as a(x), for two different numbers as x, what must be the relation between the numbers?