Today we will discuss two multiple choice questions involving energy and power. The first question appeared in the EAMCET 2009 (Engineering) question paper and the second question appeared in the EAMCET 2008 (Engineering) question paper:

**(1)** A motor of power P_{0} is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe *n* times, the power of the motor is increased to P_{1}. The ratio of P_{1} to P_{0} is

(1) *n *: 1

(2) *n*^{2}* *: 1

(3) *n*^{3}* *: 1

(4) *n*^{4}* *: 1

If the mass of water delivered per second is *m* when the power is P_{0}, we have

P_{0} α ½ *mv*^{2} where *v* is the velocity of water

[We do not equate P_{0} to ½ *mv*^{2} since the efficiency of the motor will not be 100%].

To increase the rate of flow of water through the same pipe *n* times, the velocity of water has to be made *n* times. The mass of water delivered per second then is *nm*. Therefore we have

P_{1} α ½ *nm *(*nv*)^{2}

From the above we obtain

P_{1}/ P_{0} = *n*^{3} [Option (3)].

**(2)** A river of salty water is flowing with a velocity 2 ms^{–1}. If the density of water is 1.2 g cm^{–3}, then the kinetic energy of each cubic metre of water is

(1) 2.4 J

(2) 24 J

(3) 2.4 kJ

(4) 4.8 kJ

The density of the water in the river is 1.2 g cm^{–3}, which is equal to 1200 kg m^{–3}. Mass of one cubic metre of the water is 1200 kg and its kinetic energy *E* is given by

*E* = ½ *mv*^{2} = ½ ×1200×2^{2} = 2400 J = 2.4 kJ.