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. \(M^{0}L^{0}T^{0}K^{-1}\)

Answer : Option D

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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

Answer : Option D

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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

Answer : Option C

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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

Answer : Option B

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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. \(M^{1}L^{1}T^{0}\)

Answer : Option A

Explanation :

\(\frac{\alpha z}{k\theta }=M^{0}L^{0}T^{0}\)

\(\therefore \alpha =\frac{k\theta }{z}\ and\ P=\frac{\alpha}{\beta }\)

\(\therefore \beta =\frac{\alpha }{p}=\frac{k\theta }{pz}\)


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