To find the average value of the output voltage in a half wave rectifier, we need to first understand the working principle of a half wave rectifier.

Working Principle:
A half wave rectifier is a circuit that converts the negative half of an alternating current (AC) input signal into a unidirectional current. It uses a diode, which allows current to flow in only one direction.

Given:
Input voltage, Vin = 200sin(300t)

To find the average value of the output voltage, we need to find the average value of the positive half of the input waveform.

Average Value Calculation:
The average value of a waveform can be found by integrating the waveform over one complete cycle and dividing it by the period.

1. Find the expression for the positive half of the input waveform:
The given input voltage is a sine wave, which is positive for 0 to π radians and negative for π to 2π radians. So, we need to consider the positive half of the waveform.

Vin_pos = 200sin(300t) (0 ≤ t ≤ π/300)
= 0 (π/300 ≤ t ≤ 2π/300)

2. Calculate the average value:
The average value of a waveform can be calculated using the following formula:

Vavg = (1/T) ∫(0 to T) f(t) dt

Since we are considering the positive half of the waveform, the period T will be π/300.

Vavg = (1/π/300) ∫(0 to π/300) 200sin(300t) dt
= (300/π) ∫(0 to π/300) 200sin(300t) dt
= (300/π) [-cos(300t)] (0 to π/300)
= (300/π) [1 - cos(π)]
= (300/π) [1 + 1]
= (300/π) * 2
= 600/π
≈ 191.013 V

Therefore, the average value of the output voltage in the given half wave rectifier is approximately 191.013 V.

Since none of the provided options match the calculated average value, it seems there might be an error in the given options or in the calculation.