Question

A Water pump can lift 60 litres of water per minute in a tank. If the P.E of water stored is 21.6 kJ, what is the height at which the water tank is situated? (1l =1 kg)

Answer 1

AnswEr :

• Water tank is situated 36 m high .

GivEn :

• Mass(m)= 60 kg [ 1kg = 1 L ; 60kg = 60 L]

• Time taken(t) = 1 min = 60 s

• Work done(W) = 21.6 kJ = 21.6 × 10³ J

• Gravitational field (g) = 10 m/s²

To find :

• Height at which the water tank is situated = ?

Solution :

According to the formula of work done,

$\dashrightarrow \sf \: \: \: Work \: done = m \times g \times h$

$\dashrightarrow \sf \: \: \:21.6 \times {10}^{3} = 60 \times 10 \times h$

$\dashrightarrow \sf \: \: \:h = \dfrac{21.6 \times {10}^{3} }{60 \times 10}$

$\dashrightarrow \sf \: \: \: \dfrac{21.6 \times 10}{6}$

$\dashrightarrow \sf \: \: \:h = \dfrac{216}{6}$

$\dashrightarrow \sf \: \: \:{ \underline{ \boxed{ \bf{ \purple{h = 36 \: m}}}}} \ \bigstar$

Therefore, water tank is situated 36 m high .

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$\dag \large \: { \underline{ \underline{ \sf{ \orange{Additional \: information :-}}}}}$

• Work is a factor which depends on the force which is applied on the body/object.

• In simple words, whenever energy is transferred from 1 body/object to the another, work is done .

• Work is a Scalar quantity. [As it is the dot product of 2 vectors]

It is given by,

$\dag \large \: { \boxed{ \rm{W = mgh}}}$

where,

m = mass

g = gravity

h = height

• Joule (J) is the SI unit of work .

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