let q denote the charge on the plate of a capacitor of

Let $$Q$$ denote the charge on the plate of a capacitor of capacitance $$C.$$ The dimensional formula for $$\frac{{{Q^2}}}{C}$$ is

A. $$\left[ {{L^2}{M^2}T} \right]$$

B. $$\left[ {LM{T^2}} \right]$$

C. $$\left[ {{L^2}M{T^{ - 2}}} \right]$$

D. $$\left[ {{L^2}{M^2}{T^2}} \right]$$

Answer : $$\left[ {{L^2}M{T^{ - 2}}} \right]$$

Solution :
We know that $$\frac{{{Q^2}}}{{2C}}$$ is energy of capacitor, so it represent the dimension of energy $$ = \left[ {M{L^2}{T^{ - 2}}} \right].$$

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

Let $$Q$$ denote the charge on the plate of a capacitor of capacitance $$C.$$ The dimensional formula for $$\frac{{{Q^2}}}{C}$$ is

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-

Practice More Releted MCQ Question on
Unit and Measurement

Practice More MCQ Question on Physics Section

Let $$Q$$ denote the charge on the plate of a capacitor of capacitance $$C.$$ The dimensional formula for $$\frac{{{Q^2}}}{C}$$ is

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-

Practice More Releted MCQ Question on Unit and Measurement

Practice More MCQ Question on Physics Section

Releted MCQ Question on
Basic Physics >> Unit and Measurement

Practice More Releted MCQ Question on
Unit and Measurement