Answer

Verified

375.3k+ views

**Hint:**Use the formula for the relation between the work done and change in potential energy of an object. Use the formula for the potential energy of an object. Also use the formula for the power in terms of work done and time. First determine the work done by the motor pump from the initial and final potential energies of the water. Then calculate the power of the motor.

**Formulae used:**

The work done \[W\] is given by

\[W = - \Delta U\] …… (1)

Here, \[\Delta U\] is the change in potential energy.

The potential energy \[U\] of an object is given by

\[U = mgh\] …… (2)

Here, \[m\] is the mass of the object, \[\gamma \] is acceleration due to gravity and \[h\] is the height of the object from the ground.

The power \[P\] is given by

\[P = \dfrac{W}{t}\] …… (3)

Here, \[W\] is the work done and \[t\] is time.

**Complete step by step answer:**

We have given that the mass of water lifted by the motor pump in one minute is \[300\,{\text{kg}}\].

\[m = 300\,{\text{kg}}\]

\[\Rightarrow t = 1\,{\text{min}}\]

The depth of the well is \[20\,{\text{m}}\] and the height up to which the water is being delivered is \[20\,{\text{m}}\].

\[d = 20\,{\text{m}}\]

\[\Rightarrow h = 20\,{\text{m}}\]

We have asked to calculate the power of the pump.Let us first calculate the work done by the pump.The initial potential energy of the water is zero.

\[{U_i} = 0\,{\text{J}}\]

The final potential energy of the water is given by

\[{U_f} = mg\left( {d + h} \right)\]

According to equation (1), the work done by the motor pump is

\[W = - \left( {{U_i} - {U_f}} \right)\]

Substitute \[0\,{\text{J}}\] for \[{U_i}\] and \[mg\left( {d + h} \right)\] for \[{U_f}\] in the above equation.

\[W = - \left[ {\left( {0\,{\text{J}}} \right) - \left( {mg\left( {d + h} \right)} \right)} \right]\]

\[ \Rightarrow W = mg\left( {d + h} \right)\]

Substitute \[mg\left( {d + h} \right)\] for \[W\] in equation (3).

\[P = \dfrac{{mg\left( {d + h} \right)}}{t}\]

Substitute \[300\,{\text{kg}}\] for \[m\], \[9.8\,{\text{m/}}{{\text{s}}^2}\] for \[g\], \[20\,{\text{m}}\] for \[d\], \[20\,{\text{m}}\] for \[h\] and \[1\,{\text{min}}\] for \[t\] in the above equation.

\[P = \dfrac{{\left( {300\,{\text{kg}}} \right)\left( {9.8\,{\text{m/}}{{\text{s}}^2}} \right)\left( {20\,{\text{m}} + 20\,{\text{m}}} \right)}}{{1\,{\text{min}}}}\]

\[ \Rightarrow P = \dfrac{{\left( {300\,{\text{kg}}} \right)\left( {9.8\,{\text{m/}}{{\text{s}}^2}} \right)\left( {20\,{\text{m}} + 20\,{\text{m}}} \right)}}{{60\,{\text{s}}}}\]

\[ \Rightarrow P = 1960\,{\text{J}}\]

\[ \therefore P = 1.96\,{\text{kJ}}\]

Therefore, the power of the pump is \[1.96\,{\text{kJ}}\].

**Hence, the correct option is B.**

**Note:**The students should not forget to convert the unit of time in the SI system of units as all the units used in the formula are in the SI system of units. Also the students may directly use the formula for potential energy. But the students should keep in mind that the work done is equal to the negative of change in potential energy and not equal to the potential energy.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

The provincial president of the constituent assembly class 11 social science CBSE

Gersoppa waterfall is located in AGuyana BUganda C class 9 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The hundru falls is in A Chota Nagpur Plateau B Calcutta class 8 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE