161.  Equation of $$l_{t}=l_{0}\left [ 1+\alpha \left ( T_{2}-T_{1} \right ) \right ]$$ find out the dimensions of the coefficient of linear expansion $$\alpha$$ suffix.

A. $$M^{0}L^{0}T^{1}K^{1}$$

B. $$M^{0}L^{1}T^{1}K^{1}$$

C. $$M^{1}L^{1}T^{0}K^{1}$$

D. $$M^{0}L^{0}T^{0}K^{-1}$$

162.  Test if the following equation are dimensionally correct (S = surface tension $$\rho$$ = density P = pressure v = volume n = coefficient of viscosity r = radius)

A. $$h=\frac{2S\cos \theta }{\rho gr}$$

B. $$v=\sqrt{\frac{p}{\rho }}$$

C. $$v=\frac{\pi pr^{4}t}{8nl}$$

D. All of the above

163.

Match list - I with list - II

List - I                  List - II

(1) Joule             (a) henry $$\times$$ ampere/sec
(2) Walt               (b) coulomb $$\times$$ volt
(3) volt                (c) metre $$\times$$ ohm
(4) Resistivity      (d) $$(ampere)^{2} \times ohm$$

A. b,d,c,a

B. c,a,b,d

C. b,d,a,c

D. b,c,a,d

164.

Match column - I with column - II

Column -I                       Column - II

(1) capacitance              (a) $$M^{1}L^{1}T^{-3}A^{-1}$$
(2) Electricfield               (b) $$M^{1}L^{2}T^{-1}$$
(3) planck’s constant      (c) $$M^{-1}L^{-2}T^{4}A^{2}$$
(4) Angular momentum  (d) $$M^{1}L^{2}T^{-1}$$

A. a,c,b,d

B. c,a,d,b

C. c,a,b,d

D. a,b,d,c

165.  In the relation $$P=\frac{\alpha }{\beta }e^{\frac{-\alpha z}{k\theta }}$$, P is pressure, z is distance, k is boltzmann constant and $$\theta$$ is the temperature. The dimensional formula of $$\beta$$ will be

A. $$M^{0}L^{2}T^{0}$$

B. $$M^{1}L^{0}T^{1}$$

C. $$M^{1}L^{1}T^{-1}$$

D. $$M^{1}L^{1}T^{0}$$

$$\frac{\alpha z}{k\theta }=M^{0}L^{0}T^{0}$$
$$\therefore \alpha =\frac{k\theta }{z}\ and\ P=\frac{\alpha}{\beta }$$
$$\therefore \beta =\frac{\alpha }{p}=\frac{k\theta }{pz}$$
$$=M^{0}L^{2}T^{0}$$