A galvanometer whose resistance is 50Ω deflects full scale for a potential difference 100mV across in terminals. How can it be converted into a voltmeter of 50V range

Based upon the meter's resistance being 50 ohms and the full-scale voltage equal 100mV, the full-scale current through the meter is 2 mA.

To have a 50 volt range meter, place fixed resistors and a variable resistor (potentiometer) in series with the meter.

The fixed resistors would be 22,000 and 2,000 ohms, respectively; I would use a 1,000 variable resistor, which may be used to determine full-scale deflection @ 50 volts.

I'll make this harder. Suppose that you didn't know R of the meter. Propose an experment to determine R?

Place an ammeter and a 50k variable resistor in series with the galvanometer. Then decrease the resistance until the galvanometer shows full-scale deflection. The ammeter would show the current at full-scale deflection.