Question

If E = Ae-Bx where E is energy and x is length then
dimension of A is same as energy & B is,
length
dimension of Ais same as power x time & Bis valamitvtine
dimension of A is same as ML2T-2 & B is L-1
None of these​

Answer 1

Given,

equation of energy is given by, E = Ae^(-Bx) , where E is energy and x is length.

To check,

dimension of A and B.

from dimensional analysis,

dimension of E = dimension of A

therefore, dimension of A is same as energy.i.e., [ML²T¯²]

power of exponential function is dimensionless quantity. so, dimension of Bx = dimensionless quantity.

⇒dimension of B × dimension of x = 1

⇒dimension of B = 1/[L] = [L¯¹]

therefore dimension of B is [L¯¹]

option (c) dimension of A is same as ML²T¯² & B is L¯¹, is correct choice.