Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
The pair of physical quantities that have the same dimensions are (1) Reynold number and coefficient of friction (2) Curie and frequency of light wave (3) Latent heat and gravitational potential (4) Planck's constant and torqueA) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: A
Solution :
Reynold number is simply a number while coefficient of friction is the ratio of two forces: Hence, both quantities are dimeusionless. Curie is the unit for expressing rate of disintegration. Hence, its dimension is\[[{{T}^{-1}}]\]; same as that of frequency. Latent heat; \[[L]=\frac{[Q]}{[M]}\] \[=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[M]}\] \[=[{{L}^{2}}{{T}^{-2}}]\] \[[V]=\frac{[GM]}{[r]}\] \[=\frac{[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}M]}{[L]}\] \[=[{{L}^{2}}{{T}^{-2}}]\] Further, Planck's constant have got the dimensions of angular momentum L while torque t possesses the dimensions of\[\left[ \frac{dL}{dt} \right]\]. Thus, options (1), (2) and (3) are correct.
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