Discussion
The dimension of X in the equation, \(F = 6\pi\eta X\) is
( F - Force; η -Coefficient of viscosity)
Answer: A
The dimension of X is \(M^{0}L^{2}T^{-1}\).
Rearrange for X; the number \(6\pi\) is dimensionless. Force is \(MLT^{-2}\), and the coefficient of viscosity (from \(F = \eta A\frac{dv}{dx}\)) is \(ML^{-1}T^{-1}\).
\[ \begin{aligned} [X] &= \frac{[F]}{[\eta]} = \frac{MLT^{-2}}{ML^{-1}T^{-1}} \\ &= M^{0}L^{2}T^{-1} \end{aligned} \]
So X has the dimensions of area per second (in Stokes' law \(F = 6\pi\eta rv\), X stands for the product rv). \(ML^{2}T^{-2}\) is energy, \(ML^{2}T^{-1}\) is angular momentum, and the other two have the wrong power of T or L.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development