In the circuit shown, a voltmeter of internal resistance 'R' when connected across B and C, reads $\frac{100}{3}\text{ volts}$. Neglecting the internal resistance of the cell, the value of 'R' is

Internal resistance of voltmeter is R.

Therefore effective resistance across B and C,R′ is given by

$\frac{1}{R^{\text{'}}}=\frac{1}{R}+\frac{1}{50}\Rightarrow R\text{'}=\frac{50+R}{50R}$

According to Ohm's law

$V^{\text{'}}=I{R}^{\text{'}}$

$\frac{100}{3}=I·\frac{50R}{50+R}$

Now, considering the total circuit

$R^{\text{'}\text{'}}=50+\frac{50R}{50+R}$

$V^{\text{'}\text{'}}=I{R}^{\text{'}\text{'}}$

$\Rightarrow 100=\frac{100}{3}\frac{50+R}{50R}\frac{2500+100R}{50+R}\Rightarrow R=50k\Omega$