Question

where m is linear mass density and A is force.
Two quantities A and B are related by the rela
The dimensions of B will be (ECET2012)
(A) same as that of latent heat
(C) same as that of work
(B) same as that of pressure
(D) same as that momentum​

Answer 1

answer : option (a) same as that of latent heat

explanation : The quantity m is linear mass density.

means, dimension of m = dimension of mass/dimension of length [ as linear mass density= mass/length]

= [M]/[L] = [ML-¹]

again, A is the force.

so, dimension of A = dimension of force

= dimension of mass × dimension of acceleration [ as we know, force = mass × acceleration ]

= [M][LT-²]

= [MLT-²]

now, relation , m = A/B

so, B = A/m

or, dimension of B = dimension of {A/m}

= [MLT-²]/[ML-¹]

= [L²T-²]

now options are : pressure = [ML-¹T-²]

latent heat = [L²T-²]

work = [ML²T-²]

hence, dimension of B = dimension of latent heat .

hence, option (a) is correct choice.