Question

For the equation F ∝ A^a v^b d^c , where F is the force, A is the area, v is the velocity and d is the density, the values of a, b and c are respectively 

(A) 1, 2, 1 

(B) 2, 1, 1 

(C) 1, 1, 2 

(D) 0, 1, 1

Answer 1

Answer is (A) 1, 2, 1

[M¹L¹T^-2] = [L²]^a [L¹T^-1]^b [M¹L^-3]^c 

= [L^2a][L^bT^-b] [M^cL^-3c] 

= [M^cL^{2a + b -3c} T^-b]

Comparing powers of M, L and T, 

c = 1, 2a + b - 3c = 1,

-b = - 2

∴ b = 2

2a + 2 - 3(1) = 1

∴ 2a = 2

∴a = 1