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
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
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) \((ampere)^{2} \times ohm\)
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) \(M^{1}L^{2}T^{-1}\)
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 :
\(\frac{\alpha z}{k\theta }=M^{0}L^{0}T^{0}\)
\(\therefore \alpha =\frac{k\theta }{z}\ and\ P=\frac{\alpha}{\beta }\)
\(\therefore \beta =\frac{\alpha }{p}=\frac{k\theta }{pz}\)
\(=M^{0}L^{2}T^{0}\)