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.

A sonometer wire 36 cm long vibrates with a fundamental frequency of 280Hz , when it is under tension of 24.5 N . Calculate mass per unit length of wire.

[L^1M^1T^-2] Is the dimensional formula for

[L^2 M^1 T^(-2)] is the dimensional formula for

If the dimensional formula for the physical quantity is [M^(1)L^(2)T^(-2)] then the physical quantity is ______ .

A long straight conductor AB, carrying a current of 25 A is fixed horizontally. Another long conductor XY is kept parallel to AB at a distance of 4mm, in air. Conductor XY is free to move and carries current 1. Then the magnitude and direction of current I forwhich the magnetic repulsion just balances the weight of conductor XY is (Mass per unit length for conductor XY is 5 xx 10^(-2) Kg//m) .

From the terrace of building of height H, you dropped a ball of mass m. It reached the ground with speed v. Is the relation mgH = frac(1)(2)mv^2 applicable exactly ? If not, how can you account for the difference ? Will the ball bounce to the same height from where it was dropped?

At what tension a wire of length 1 m and mass 2 gram will be in resonance with frequency of 350 Hz .

A uniform string of length L and mass M is fixed at both end while it is subject to a tension T . It can vibrate at frequencies v given bby the formula (where, n=1,2,3,………..)

Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n_(1) and the other with frequency n_(2) the ratio n_(1)//n_(2) is given by