Question

Problem 17. What
are the dimensions of a and b in the relation
$f = a + bx \: where f is the force and x is relation$
​

Answer 1

Answer:

By dimensional analysis we consider both the LHS and RHS have the same dimensions.

F=a+bx

In the given equation the LHS is F which stands for force

[F] = [MLT^-2 ]

now in RHS we have two constants a & b , by additive property we find that a and F will have the same dimension .

Thus [a] = [ MLT^ -2]

Now for…. bx , we know x is distance so it has dimension x= [ L ]

Thus we get bx = [ MLT ^-2]

=> b[ L ]= [ MLT ^-2]

=>. b= [ MT ^-2]

a= [MLT ^-2 ] & b=[MT ^-2 ]