The high resistance voltmeter means, that current will flow through it. Hence, there is no potential difference across it. So, the reading shown by the high resistance voltmeter can be taken as the emf of the cell.
The internal resistance of a cell depends on
(i) the concentration of electrolyte and
(ii) distance between the two electrodes.
The emf of cell, E = 2.2 V .
The terminal voltage across cell when 5 Ω resistance R is connected across it, V= 1.8 V
Let internal resistance = r
Internal resistance, r= r(E/V -1)
= 5(2.2/1.8-1) = 5 x 0.4/1.8 = 2/1.8 =10/9 Ω