To make voltmeter to ammeter ..shunt to be added parallel ..hence ..1/r=1/rg+1/rsthen we have ...{(800*10^-3)/1/r}=100*10^-3so we ..will get rs = 10ohm

To convert a millivoltmeter of resistance 40 Ω and range 800 mV into a galvanometer of range 100 mA, a shunt resistance needs to be connected in parallel with the galvanometer.

Step 1: Determine the current range of the millivoltmeter
The millivoltmeter has a range of 800 mV, which means it can measure voltages up to 800 mV. Since the millivoltmeter has an internal resistance of 40 Ω, we can use Ohm's Law to find the current range.

Using Ohm's Law (V = IR), we can rearrange the formula to solve for the current (I):
I = V/R

Substituting the values, we get:
I = (800 mV) / (40 Ω)
I = 20 mA

Therefore, the current range of the millivoltmeter is 20 mA.

Step 2: Determine the shunt resistance
To convert the millivoltmeter into a galvanometer with a current range of 100 mA, a shunt resistance needs to be connected in parallel with the galvanometer.

The formula to calculate the shunt resistance is:
Rs = (Rm * Im) / (Ig - Im)

Where:
Rs = shunt resistance
Rm = internal resistance of the millivoltmeter
Im = current range of the millivoltmeter
Ig = desired current range of the galvanometer

Substituting the values, we get:
Rs = (40 Ω * 20 mA) / (100 mA - 20 mA)
Rs = (800 mV) / (80 mA)
Rs = 10 Ω

Therefore, the shunt resistance that needs to be connected is 10 Ω.

Step 3: Verify the answer
To verify the answer, we need to check if the current range of the converted galvanometer is indeed 100 mA.

Using Ohm's Law again, we can calculate the current (I) flowing through the galvanometer:
I = V/R
I = 800 mV / (40 Ω + 10 Ω)
I = 800 mV / 50 Ω
I = 16 mA

Since the calculated current is less than the desired current range of 100 mA, we can conclude that the answer is correct.

Therefore, the resistance to be connected as a shunt is 10 Ω (option 'A').