Explanation

In a potentiometer, the EMF of a cell is directly proportional to the balancing length.

$$ \frac{E_1}{E_2} = \frac{L_1}{L_2} $$

Given,

$$ L_1 = 200\,cm,\quad L_2 = 150\,cm $$

The least count of the scale is $1\,cm$. Hence, the absolute error in each length measurement is

$$ \Delta L_1 = \Delta L_2 = 1\,cm $$

For a ratio, the fractional error is given by

$$ \frac{\Delta R}{R} = \frac{\Delta L_1}{L_1} + \frac{\Delta L_2}{L_2} $$

Substituting values,

$$ \frac{\Delta R}{R} = \frac{1}{200} + \frac{1}{150} $$

$$ \frac{\Delta R}{R} = 0.005 + 0.00667 = 0.01167 $$

Percentage error is

$$ \%\,\text{error} = 0.01167 \times 100 $$

$$ \%\,\text{error} = 1.17\% $$

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