Question
Physics Question on physical world
In the following equation, x, t and F represent respectively, displacement, time and force : F=a+bt+c+dx1+Asin(ωt+ϕ). The dimensional formula for A?d is
A
T−1
B
L−1
C
M−1
D
TL−1
Answer
L−1
Explanation
Solution
F=a+bt+c+dx1+Asin(ωt+ϕ).
As sin(?t+ϕ) is dimensionless, therefore A has dimensions of force.
∴[A]=[F]=[MLT−2]
As each term on RHS represents force
∴[c+dx1]=[F]
[c1]=[F]
∴[c]=[F]1=[MLT−2]1=[M−1L−1T2]
As c is added to dx, therefore dimensions of c is same that of dx.
∴[dx]=[c]
or [d]=[x][c]=[L][M−1L−1T2]=[M−1L−2T−2]
The dimensional formula for A?d is
[A?d]=[MLT2][M−1L−2T−2] =[L−1]