Question

Given ,force=alpha/density+beta^3 , what is the dimensions of alpha and beta?

Answer 1

Given,

Force = alpha/density + beta³

By principal of homogenety, we know that only like quantities can be added or subtracted. So, the

dimensions of alpha/density = dimensions of beta³

Now,

[Force] = [MLT-²]

[Density] = [ML-³]

A/Q:-

[Force] =[alpha]/[density]

[MLT-²] = [alpha]/ [ML-³]

[MLT-²]×[ML-³] = [alpha]

[M²L-²T-²] = [alpha]

Again, According to principal of homogenety,

[alpha]/[density] = [beta³]

[M²L-²T-²]/[ML-³] = [beta³]

[MLT-²] =[beta³]

[beta] = [MLT-²]^⅓

Cheers!