if the dimensions of a physical quantity are given by m pow

If the dimensions of a physical quantity are given by $${M^a}{L^b}{T^c},$$ then the physical quantity will be

A. velocity if $$a = 1,b = 0,c = - 1$$

B. acceleration if $$a = 1,b = 1,c = - 2$$

C. force if $$a = 0,b = - 1,c = - 2$$

D. pressure if $$a = 1,b = - 1,c = - 2$$

Answer : pressure if $$a = 1,b = - 1,c = - 2$$

Solution :
Pressure $$ = \frac{{ML{T^{ - 2}}}}{{{L^2}}} = \left[ {M{L^{ - 1}}{T^{ - 2}}} \right]$$
$$ \Rightarrow a = 1,b = - 1,c = - 2.$$

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. $$M{L^2}{T^{ - 1}}$$

View Answer

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

View Answer

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. $$1.732 \times {10^{ - 6}}{m^3}$$

View Answer

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. $${M^{ - 1}}{L^1}{T^2}$$

View Answer

If the dimensions of a physical quantity are given by $${M^a}{L^b}{T^c},$$ then the physical quantity will be

Releted MCQ Question on
Basic Physics >> Unit and Measurement

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

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

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-

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Unit and Measurement

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If the dimensions of a physical quantity are given by $${M^a}{L^b}{T^c},$$ then the physical quantity will be

Releted MCQ Question on Basic Physics >> Unit and Measurement

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

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

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-

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Releted MCQ Question on
Basic Physics >> Unit and Measurement

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Unit and Measurement