The physical quantity 'Energy Density' has th | vedclass

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Question

(D) Energy density is defined as energy per unit volume: $U = \frac{	ext{Energy}}{	ext{Volume}}$.The dimensional formula for Energy is $[ML^2T^{-2}]

Vedclass · Accepted Answer

All of these

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(D) Energy density is defined as energy per unit volume: $U = \frac{	ext{Energy}}{	ext{Volume}}$.The dimensional formula for Energy is $[ML^2T^{-2}]$ and for Volume is $[L^3]$.Thus,the dimensional formula for Energy Density is $\frac{[ML^2T^{-2}]}{[L^3]} = [ML^{-1}T^{-2}]$.Pressure is defined as force per unit area: $P = \frac{F}{A}$. Its dimensions are $\frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$.Stress is defined as restoring force per unit area: $\sigma = \frac{F}{A}$. Its dimensions are $[ML^{-1}T^{-2}]$.Young's modulus of elasticity is defined as the ratio of stress to strain: $Y = \frac{	ext{Stress}}{	ext{Strain}}$. Since strain is dimensionless,the dimensions of $Y$ are the same as stress,which is $[ML^{-1}T^{-2}]$.Since all the given quantities have the same dimensional formula $[ML^{-1}T^{-2}]$,the correct option is $D$.

Column-$I$	Column-$II$
$(A)$ Electrical resistance	$(p)$ $M L^3 T^{-3} A^{-2}$
$(B)$ Electrical potential	$(q)$ $M L^2 T^{-3} A^{-2}$
$(C)$ Specific resistance	$(r)$ $M L^2 T^{-3} A^{-1}$
$(D)$ Specific conductance	$(s)$ None of these

The physical quantity 'Energy Density' has the same dimensional formula as

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Match the following two columns:

Column-$I$ Column-$II$

$(A)$ Electrical resistance $(p)$ $M L^3 T^{-3} A^{-2}$

$(B)$ Electrical potential $(q)$ $M L^2 T^{-3} A^{-2}$

$(C)$ Specific resistance $(r)$ $M L^2 T^{-3} A^{-1}$

$(D)$ Specific conductance $(s)$ None of these

The dimensional formula of capacitance is . . . . . . . Take $Q$ as the dimensional formula of charge.

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