A full sphere subtends a solid angle of 4π steradians at its center.
205
A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is 58.7 cm and the density of iron is 7.87 g cm^-3. What is the approximate inner diameter of the shell?
Using the relation between submerged volume and density, the inner radius computes to about 28 cm, so inner diameter ≈ 56 cm, corresponding to option (a).
206
A small tiny lead shot is gently dropped on the surface of a viscous liquid. The velocity of the lead shot will
1 m/s^2 = 12960 km/hr^2, so 1.5×12960 = 19440 km/hr^2; hence option D.
208
Two capillary tubes of same diameter are put vertically, one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 60 and 50 dyn/cm respectively. Ratio of heights of liquids in the two tubes h1/h2 is:
Rubber is nearly incompressible so its Poisson's ratio is approximately 0.5.
210
Two rods of different materials having coefficients of thermal expansion α1 and α2 and Young's moduli Y1 and Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. If α1 : α2 = 2 : 3, the thermal stresses developed in the two rods are equal provided Y1 : Y2 is equal to
