Check the correctness of the equation\(\frac { 1 }{ 2 } \)mv² = mgh using dimensional analysis method.

The force F acting on a body moving in a circular path depends on mass of the body (m), velocity (v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method. (Take the value of k = 1)

A capacitor of capacitance C = 3.0 ± 0.1\(\mu \)F is charged to a voltage of V = 18 ± 0.4 Volt. Calculate the charge Q [Use Q = CV].

Convert 76 cm of mercury pressure into Nm^-2 using the method of dimensions.

Explain the principle of homogeniety of dimensions. What are its uses? Give example