Question

When dimensions of a given physical quantity are given, the physical quantity is unique.
A. The statement and its converse both are true.
B. The statement and its converse both are false.
C. The statement is false but its converse is true.
D. The statement is true but its converse is false.

Answer 1

Final Answer : C : The statement is false, but it's converse is true.

Steps:
1) Statement :
When Dimension if a physical quantity is given, then the physical quantity is unique :
False:
Reason:
Two Physical quantities can have sane dimension whose notion is different physically.

For Example : Momentum and Impulse have same Dimension but their physical meaning is different.
Both have dimension : M/(LT)

Converse : When physical quantity is given, then it's dimension is unique.
True :
Dimension of a given physical quantity is always unique since we can't change its nature which is it's dimension.

For Example : Velocity always has dimension
L/T which can never Change unless we chang^ the physical quantity.