Question

A scientist uses a water tank located at a height of 27m from the ground to generate electric power to run a 50W bulb. He installs a water driven wheel generator on the ground.if the capacity of tank is 500L and efficiency of generator is 80 °/• , then the time for which he can keep the bulb on with s full tank, is
1) P=VR
2)P=V^2÷R
3)P=I^2÷R
4)P=VI

Answer 1

height of water tank, h = 27m

capacity of water tank, V = 500L = 500 × 1000 ml

so, mass of water is available in the tank, m = 500 × 1000 ml × 1g/ml = 500000g = 500 kg

so, potential energy of water, P.E = mgh

= 500kg × 10 m/s² × 27m

= 135000 J

electric power of generator = 50W

efficiency of generator = 80% of 50W

= 80/100 × 50

= 40 W

now, time taken to full the tank, t = potential energy of water/efficiency of generator

= 135000/40 sec

= 13500/4 sec

= 135 × 25 sec

= 3375 sec

= 56 min 15 sec