Question

Which one of the following represents the correct dimensions of the coefficient of viscosity?

A. $$M{L^{ - 1}}{T^{ - 1}}$$  
B. $$ML{T^{ - 1}}$$
C. $$M{L^{ - 1}}{T^{ - 2}}$$
D. $$M{L^{ - 2}}{T^{ - 2}}$$
Answer :   $$M{L^{ - 1}}{T^{ - 1}}$$
Solution :
$$\eqalign{ & {\text{From Stokes law}}\,F = 6\pi \eta rv \Rightarrow \eta = \frac{F}{{6\pi rv}} \cr & \therefore \eta = \frac{{ML{T^{ - 2}}}}{{\left[ L \right]\left[ {L{T^{ - 1}}} \right]}} \Rightarrow \eta = \left[ {M{L^{ - 1}}{T^{ - 1}}} \right] \cr} $$

Releted MCQ Question on
Basic Physics >> Unit and Measurement

Releted Question 1

The dimension of $$\left( {\frac{1}{2}} \right){\varepsilon _0}{E^2}$$  ($${\varepsilon _0}$$ : permittivity of free space, $$E$$ electric field)

A. $$ML{T^{ - 1}}$$
B. $$M{L^2}{T^{ - 2}}$$
C. $$M{L^{ - 1}}{T^{ - 2}}$$
D. $$M{L^2}{T^{ - 1}}$$
Releted Question 2

A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$   where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-

A. resistance
B. charge
C. voltage
D. current
Releted Question 3

A cube has a side of length $$1.2 \times {10^{ - 2}}m$$  . Calculate its volume.

A. $$1.7 \times {10^{ - 6}}{m^3}$$
B. $$1.73 \times {10^{ - 6}}{m^3}$$
C. $$1.70 \times {10^{ - 6}}{m^3}$$
D. $$1.732 \times {10^{ - 6}}{m^3}$$
Releted Question 4

Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$     where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-

A. $${M^0}{L^0}{T^0}$$
B. $${M^{ - 1}}{L^{ - 1}}{T^{ - 1}}$$
C. $${M^0}{L^2}{T^0}$$
D. $${M^{ - 1}}{L^1}{T^2}$$

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