Obtain the formula `t=ksqrt(l/g)` by the method of dimensions.

State and obtain Stokes's law by the method of dimensions

Derive the folowing relation by the method of dimensions v=sqrt(T/mu) T=Tension, mu =mass per unit length.

The velocity of a freely falling body is a function of the distance fallen through (h) and acceleration due to gravity g . Show by the method of dimensions that v = Ksqrt(gh) .

The time period 'T' of a body executing SHM may be supposed to depend upon (i) the amplitude 'A' , (ii) the force constant 'k' and (iii) the mass 'm' . Deduce by the method of dimensions the formula for T.

The frequency of vibration (v) of a string may depend upon length (I) of the string, tension (T) in the string and mass per unit length (m) of the string. Using the method of dimensions, derive the formula for v.

Out of the formulae y =a sin 2pi t//T and y = a sin upsilon t for the displacement y of particle undergoing a periodic motion, rule out the wrong formula on the basis of dimensions. Symbols have standard meaning.

Assertion : The time period of a pendulum is given by the formula, T=2pisqrt(g//l) . Reason : According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.

The number of variables in the formula T=2pisqrt((l)/(g)) is _____

In the formula T=2pisqrt((l)/(g)),T is ____proportional to sqrt(l) .