Question

An electric motor of power 100 W is used to drive the stirrer in a water bath. If 50% of the energy supplied to the motor is spent in stirring the water. Calculate the work done on the water in one minute.
A. 6000 J
B. 50 J
C. 3000 J
D. 100 J

Answer 1

Hint: Use the relation between power, work done and time. Calculate the total energy produced by the motor using the given power. We have given that 50% of the energy is spent in stirring the water. Calculate 50% of the total energy supplied which is the work done on the water by the motor.

Formula used:
\[W = P \times t\]
Here, P is power and t is the time.

Complete step by step answer:
We know the relation between work done and power,
\[ \Rightarrow W = P \times t\]
Here, P is the power and t is the time.
Now, the total energy produced by the motor is the work done by the motor. Therefore, we calculate the work done by the motor as follows,
\[ \Rightarrow W = \left( {100\,W} \right)\left( {1\,\min } \right)\left( {\dfrac{{60\,s}}{{1\,\min }}} \right)\]
\[ \Rightarrow W = 6000\,J\]
We have given, 50% of the total energy is spent in stirring the water. Therefore, the work done on water by the motor is,
\[ \Rightarrow{W_{spent}} = \left( {50\% } \right)W\]
\[ \Rightarrow {W_{spent}} = \left( {0.5} \right)\left( {6000\,J} \right)\]
\[ \therefore {W_{spent}} = 3000\,J\]

So, the correct answer is option (C).

Note: Remember the units of power and energy. The S.I. unit of power is watt and S.I. unit of energy and work done is joule. To determine the work done from power and given time, the time should be in seconds and not in minutes. In case of energy supplied to the electric component is given, then it should be taken as work.