Units and Dimensions 1) Find the dimensions of the following. i) Force ii) Power iii) Permittivity of a vacuum 2) Using dimensional analysis, Show that, 1 J o u l e = 1 0 7 e r g 3) Show that the given below equation is dimensionally correct equation. v = u + a t 4) Write the C.G.S. units of the following. i) Universal gravitational constant ii) Acceleration due to gravity iii) Force 5) Find the dimensions of length in terms of force, universal gravitational constant and mass. (Consider F G and m as basic fundamental quantities.) Note: For the detailed solution, please visit the next blog. Below are only answers. Answer: 1) i) F = [ M 1 L 1 T − 2 ] ii) P = [ M 1 L 2 T − 3 ] iii) ε 0 = [ M − 1 L − 3 T 4 I 2 ] 3) i) G = g . s c m 3 ii) g = s 2 c m iii) F = s 2 g . c m 5) L = [ G 1 / 2 M 1 F − 1 / 2 ]
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