Question

The dimensional formula of the product of two physical quantities P and Q is MLT-. The dimensional formula of P/Q is MT-2. P and Q respectively are ​

Answer 1

The dimensional formula of the product of two physical quantities P and Q is ML^2 T^(-2). The dimensional formula of P//Q is ML^0 T^(-2). Then what are the units of physical quantities P and Q. ∴ P and Q are respectively the force and the displacement, hence their units are newton and metre.






P×Q=ML
2
T
−2


Q
P
​
=MT
−2


Let: P=M
A
l
B
T
C
and Q=M
a
l
b
T
c


P×Q=M
A+a
l
B+b
T
C+c
=M
1
l
2
T
−2

A+a=1;B+b=2;C+c=−2

Q
P
​
=M
A−a
l
B−b
T
C−c
=MT
−2

A−a=1;B−b=0;C−c=−2

⇒A=1,a=0B=b=1,C=−2,c=0

So, P=MlT
−2
→force
Q=M
0
l
1
T
0
→displacement