Assuming the petrol burnt (per hour) in driving a motor boat veries as the cube of its velocity, show that the most economical speed when going against the current of `c` miles per hour is `((3c)/2)` miles per hour.

A boat takes 1.6 hours longer to go 36kms up a river than down the river. If the speed of the water current is 4 km per hr, what is the speed of the boat in still water?

A currrent I is passed through a silver strip of width d and area of cross section A. The number of free electrons per unit volume is n. (a) Find the drift velocity v of the electrons. (b) If a magnetic field B exists in the region as shown in what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will be the potential diference developed across the width of the conductor due to the electron- accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called hall effect.

A motor boat heads upstream a distance of 24 km in a river whose current is running at 3 km per hour. The trip up and back takes 6 hours. Assuming that the motor boat maintained a constant speed, what was its speed in still water?

In an agriculture experiment, a solution containing 1 mole of a radioactive meterial (t_(1//2)=14.3 days) was injected into the roots of a plants.the plant was allowed 70 hours to settle down and then activity eas measured in its fruit. If the activity measured was 1 mu Ci what per cent of activity is transmitted from the root to the fruit in steady state?

Indian style of cooling drinking water is to keep it in a pitcher having porous walls. Water comes to the outer surface very slowly and evaporates .Most of the energy needed for evaporation is taken from the water itself and the water is cooled down. Assume that a pitcher contains 10kg water and 0.2g of water comes out per second. Assuming no backward heat transfer from the atmosphere to the water, calculate the time in which the temperature decreases by 5^(@)C . Specific heat capacity of water = 4200J kg^(-1).^@C^(-1) and latent heat of vaporization of water = 2.27 xx 10^(6)J kg^(-1)

A travelling wave is produced on a long horizontal string by vibrating an end up and down sinusoidal. The amplitude of vibration is 1.0cm and the displacement becomes zero 200 times per second. The linear mass density of the string is 0.10 kg m^(-1) and it is kept under a tension of 90 N. (a) Find the speed and the wavelength of the wave. (b) Assume that the wave moves in the positive x-direction and at t = 0 the end x= 0 is at its positive extreme position. Write the wave equation. (c ) Find the velocity and acceleration of the particle at x = 50 cm at time t = 10ms.

An electric kettle used to prepare tea, takes 2 minutes to boil 4 cups of water (1 cup contains 200 cc of water) if the room temperature is 25^@ C , (a) If the cost of power consumption is Re 1.00 per unit (1 unit = 1000 watt-hour) , calculate the cost of boiling 4 cups of water. (b) What will be the correspoinding cost if the room temprature drops to 5^@ C ?

When the sun is directly overhead, the surface of the earth receives 1.4 xx (10^3) W (m^-2) of sunlight. Assume that the light is monochromatic with average wavelength 500mn and that no light is absorbed in between the sun and the earth's surface. The distance between the sun and the earth is 1.5 xx (10^11) m. (a) Calculate the number of photons falling per second on each square metre of earth's surface directly below the sun. (b) How many photons are there in each cubic metre near the earth's surface at any instant? (c) How many photons does the sun emit per second?

A bakery owner makes two types of cakes A and B. three machines are needed for this pupose. The time in (minutes) required for each type of cake in each machine is given below. Each machines is available for atmost 6 hours per day. Assume that all cakes will be sold out every day. The bakery owner wants to make maximum pforit per day by making Rs. 7.5 from type A and Rs. 5 from type B. a Write the objective function by defining suitable variables. b Write the constraints. c Find the maximum profit graphically.