Check the accurary of the relation C` = (pi eta r^4)/(2l)` for couple per unit twist (C) of a wire of length (I), radius (r) and coefficient of rigidity (h).

Check the correctness of the equation v=(K eta)/(r rho) using dimensional analysis, where v is the critical velocity eta is the coefficient of viscosity, r is the radius and rho is the density?

A wire of length L and radius r is clamped at one end. On stretching the other end of the wire with a force F, the increase in its length is 1. If another wire of same material but of length 2L and radius 2r is stretched with a force 2F, the increase in its leagth will be

Express the relation between atomic radius (r) and edge length (a) in b.c.c. unit cell.

One end of a horizontal thick copper wire of length 2L and radius 2R is weded to an end of another horizontal thin copper wire of length L and radius R .When the arrangement is stretched by applying forces at two ends , the ratio of the elongation in the thin wire to that in the thick wire is

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end fo another horizontal thin copper wire of lenth L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

A circle of radius r cm has a diameter of length (a) r cm (b) 2r cm (c) 4r cm (d) r/2c m

The rate of a flow V a of liquid through a capillary under a constant pressure depends upon (i) the pressure gradient (P/l) (ii) coefficient of viscosity of the liquid eta (iii) the radius of the capillary tube r. Show dimesionally that the rate of volume of liquid flowing per sec V∝ Pr^4 /ηl

On gradual loading , stress - strain relationship for a metal wire is as follows . Within proportionality limit , stress prop strain or, "Stress"/"strain" = a constant for the material of wire. Two wires of same material have length and radius (L,r) and (2L , r/2) . The ratio of their young's modulii is

The Young's modulus of a wire of length L and radius r is Y newton/ m^(2) . If the length of the wire is dooubled and the radius is reduced to (r )/(2) , its Young's modulus will be

The volume of a liquid (V) flowing per second through a cylindrical tube depends upon the pressure gradient (p//l ) radius of the tube (r) coefficient of viscosity (eta) of the liquid by dimensional method the correct formula is