Question

a wave function expressing the displacement (Y) as a function of its position (x) and time (t) is given as Y=Alog(bx+Ct). Which of the following has dimensions different from other:

1.YC

2.AC

3.C/b

4.bC

Answer 1

From the above eqn. According to dimensional laws for an equation,
dimensions of Y=dimension of A
And

dimensions of (bx) and dimensions of (Ct) has no dimensions Because they are inside the log function...

here M,L,T are dimensions which used to represent mass,length,tume respectively.

so Y=L , so A=L
bx has no dimension means b has inverse dimension of x which is L^-1....
Similarly Ct has no dimension means C has jnverse dimension of t which is T^-1.

From the answer options
1. YC
=L.T^-1
2. AC
=L.T^-1
3. C÷b = (T^-1)÷(L^-1)
=LT^-1
4.Cb =( T^-1)×(L^-1)
=L^-1.T^-1

Si fourth one is the odd one....and it is the answer...

option 4 is ans.

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