A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is

The correct option is 96.

To understand why this is the correct answer, let us calculate the percentage efficiency of the induction motor step-by-step.

Step 1: Calculate the Synchronous Speed ($N_s$)
The synchronous speed of an induction motor is given by the formula:

$N_s=\frac{120\times f}{P}$
where:
- $f$ is the supply frequency (50 Hz)
- $P$ is the number of poles (6)

Substituting these values into the formula:

$N_s=\frac{120\times 50}{6}=1000\text{rpm}$

Step 2: Calculate the Slip ($s$)
The rotor speed ($N$) is given as 960 rpm. The slip of the induction motor is defined as:

$s=\frac{N_s-N}{N_s}$
Substituting the speeds:

$s=\frac{1000-960}{1000}=\frac{40}{1000}=0.04$

Step 3: Relate Rotor Efficiency to Slip
The ratio of rotor mechanical power output ($P_m$) to the rotor input power ($P_g$) is given by:

$\frac{P_m}{P_g}=1-s$
Since the stator copper loss, core loss, and rotational loss of the motor are neglected:
1. The stator input power is equal to the rotor input power ($P_{\text{in}}=P_g$).
2. The mechanical output power is equal to the net output power ($P_{\text{out}}=P_m$).

Therefore, the overall efficiency ($\eta$) of the motor simplifies to:

$\eta =\frac{P_{\text{out}}}{P_{\text{in}}}=1-s$

Step 4: Calculate the Percentage Efficiency
Substituting the slip value:

$\eta =1-0.04=0.96$
Converting this decimal to a percentage:

$\text{Percentage Efficiency}=0.96\times 100\%=96\%$