Question

If a pump can lift 200 kg of water through a height of 6 m in 10 seconds, then its power is

Answer 1

Given :-

Mass of the water lifted = 200 kg

Height carried by the pump = 6 m

Time taken to carry = 10 sec

To Find :-

The power of the pump.

Analysis :-

Here we are given with the mass, height and time taken to carry the water.

Firstly find the work done by substituting the given values in it's respective formula.

Then find the power done by substituting the values such that power is equal to work done divided by the time taken.

Solution :-

We know that,

m = Mass

h = Height

w = Work done

t = Time

g = Gravity

p = Power

Using the formula,

$\underline{\boxed{\sf Work \ done=Mass \times Gravity \times Height}}$

Given that,

Mass (m) = 200 kg

Gravity (g) = 10 m/s

Height (h) = 6 m

Substituting their values,

⇒ w = mgh

⇒ w = 200 × 10 × 6

⇒ w = 2000 × 6

⇒ w = 12000 J = 1.2 × 10⁴ J

Using the formula,

$\underline{\boxed{\sf Power=\dfrac{Work \ done}{Time \ taken} }}$

Given that,

Work done (w) = 1.2 × 10⁴ J

Time (t) = 10 sec

Substituting their values,

⇒ p = 1.2 × 10⁴/10

⇒ p = 1200 W

Therefore, the power of the pump is 1200 W.