Question

Convert one dyne into Newton by using dimension method

Answer 1

The dimensional formula of Force F = [M 1 L 1 T -2 ] So a =1, b=1, c=-2 Now because Newton is in m.k.s system, we have M 1 = 1kg L 1 = 1m T1 = 1s M 2 = 1g L 2 = 1cm T2 = 1s n 1 = 1 Newton n 2 = ? Using the formula n 2 = n 1 [M 1 /M 2 ]a [L 1/L 2 ]b [T 1/T 2 ]c n 2 =1 [1kg/1g] 1[1m/1cm] 1 [1s/1s] -2 n 2 =1[1000g/1g] 1[100cm/1cm] 1 x1 n 2 =1000×100 = 100000 = 10 5 dynes