Question

What are the dimensions of 'a' and 'b' in th relation F=a+bx, where F is force and x is the distance?

Answer 1

Here,
F = a + bx
Since a is connected by addition symbol so a has dimension same as F
[F] = [a] = [MLT-2]
Let [b] = [MxLyTz]
Again bx has dimension of F
[ F]= [b][x]
=> [MLT-2] = [MxLyTz][L]
=> [MLT-2] = [MxLy+1Tz]
Comparing the powers of M L and T
x = 1
y + 1 = 1
=> y = 0
z = -2
So [b] = [MxLyTz] = [M1L0T-2]
[b] = [M1T-2]