The ratio of powers of two motors is (3 √x)/(√x+1), that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

Solution

Physics sir · 3 steps

Same well, same g, so the power ratio is just the ratio of kilograms lifted per minute.

1. Power of a pump. Each motor gives water potential energy mgh in time t, so P = mgh/t. Both motors lift water through the same h = 100 m, so g and h cancel in the ratio.

   P₁/P₂ = (m₁/t₁)/(m₂/t₂) = (300/5)/(50/2) = 60/25 = 2.4

2. Set up for x. Equate to the given form: 3√x/(√x+1) = 2.4. Cross-multiplying gives 3√x = 2.4√x + 2.4, so 0.6√x = 2.4 and √x = 4.
3. So. Squaring gives x = 16, which is option (a).

The idea to keep. When two machines do the same kind of work against the same height, compare only what differs. Here that is mass per unit time, and the common factors g and h drop out.

Answer from the NTA final answer key. Solution by PrepWiser.