The period T of a pendulum might depend on the bob's mass m, the length l and g…

Step 1. Powers. $[\text{T}] = [\text{M}]^{x}[\text{L}]^{y}[\text{L}\,\text{T}^{-2}]^{z}$. M: $x = 0$. T: $1 = -2z$, $z = -\frac{1}{2}$. L: $0 = y + z$, $y = \frac{1}{2}$.

Step 2. The form. $T = k\sqrt{l/g}$: the mass does not matter.

Step 3. (b). $\dfrac{T_2}{T_1} = \sqrt{\dfrac{l_2}{l_1}} = \sqrt{\dfrac{1.60\ \text{m}}{0.90\ \text{m}}} = 1.333$, so $T_2 = 1.90\ \text{s} \times 1.333 = 2.53\ \text{s}$.