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 velocity of sound waves 'v' through a medium may be assumed to depend on : (i) the density of the medium 'd' and (ii) the modulus of elasticity 'E' . Deduce by the method of dimensions the formula for the velocity of sound . Take dimensional constant K=1.

M.I. of a body doesn't depend upon

Derive by method of dimensions an expression for the energy (E ) of a body executing SHM assuming that this energy depends upon (i) the mass (m), (ii) the frequency (v) and the amplitude of vibration (gamma) .

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.

The mass of particle executing S.H.M. is 1 gm. If its periodic time is pi seconds, the value of force constant is :

The frequency ( nu ) of transverse wave on a string may depend upon (i) length L of string (ii) tension T in the string and (iii) mass per unit length m of the string Derive the formula for frequency with the help of dimensions.

The wavalenght (lambda) of matter waves may depends upon Planck's constant (h) mass (m) and velocity (upsilon) of the particle. Use the method of dimensions to derive the formula

Obtain an expression for the time period T of a simple pendulum. [The time period T depend upon (i) mass l of the bob (ii) length m of the pendulum and (iii) acceleration due to gravity g at the place where pendulum is suspended. Assume the constant k=2pi ]