Force F and density d are related as, F = α β + d . F ind the dimensions of α and β .

As we know that, force is defined as, F = m × a , where m and a are mass and acceleration respectively. Substituting the dimensions of mass and acceleration we get dimension of force F = MLT - 2 Also, two quantities if added should have same dimensions. Hence, the dimensional formula for β should be same as the dimensional formula for d . ⇒ β = d and d = ML - 3 1 2 = M 1 2 L - 3 2 Also, the dimensions in the L.H.S. should be equal to that in the R.H.S. Hence, ⇒ α = β F ⇒ α = M 1 2 L - 3 2 MLT - 2 ⇒ α = M 3 2 L - 1 2 T - 2

Force F and density d are related as, F = α β + d . F ind the dimensions of α and β .

As we know that, force is defined as, F = m × a , where m and a are mass and acceleration respectively. Substituting the dimensions of mass and acceleration we get dimension of force F = MLT - 2 Also, two quantities if added should have same dimensions. Hence, the dimensional formula for β should be same as the dimensional formula for d . ⇒ β = d and d = ML - 3 1 2 = M 1 2 L - 3 2 Also, the dimensions in the L.H.S. should be equal to that in the R.H.S. Hence, ⇒ α = β F ⇒ α = M 1 2 L - 3 2 MLT - 2 ⇒ α = M 3 2 L - 1 2 T - 2