Using method of dimensional analysis show that ` 1 J = 10^7` erg.

Show that 1 J = 10^7 erges.

Consider a small sphere falling through a medium. The viscous force acting on the sphere depends upon the radius (r) of the sphere, velocity (V) of the sphere and the co-efficient of viscosity (eta) of the medium. Use dimensional analysis and show that the viscous force is directly proportional to etarv . (Given : Dimensions of eta =[M^1L^-1T^-1]) .

Show that (1 kWh = 3.6 xx 10^6J ).

Explain with example how is dimensional analysis used to verify the correctness of physical equation.

Explain with example, how is dimensional analysis used to convert the unit of a physical quantity from one system to another system of units.

Define dimensions and state uses of dimensional analysis.

Assume that the speed (v) of sound in air depends upon the pressure (P) and density rho of the air and use dimensional analysis to obtain an expression for the speed of sound.

Explain with example, how dimensional analysis is used to derive the relation, n=frac(1)(2L)sqrtfrac(T)(m) where n rarr Frequency, T rarr Tension, L rarr Length, m rarr mass per unit length.

The density of mercury is 13.6 g//cm^3 using dimensional analysis express it in kg//m^3

Prove the following by the method of induction for all n in N : 3 + 7+ 11 +.. to n terms = n(2n + 1).