1.If force $F$, velocity $V$, and time $T$ are taken as fundamental quantities, find the dimensions of Mass and Surface Tension.
2.A student measures the value of $g$ using a simple pendulum. Length $L = (100 \pm 0.1)\text{ cm}$ and time for 20 oscillations $t = (40 \pm 1)\text{ s}$. Find the maximum percentage error in $g$.
3.Using Buckingham $\pi$-theorem or dimensional analysis, express the drag force $F$ on a sphere of radius $r$ moving with velocity $v$ in a fluid of density $\rho$ and viscosity $\eta$.
