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Measurement MCQs for NEET — Physics Questions with Answers

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The dimensions of Farad are , where Q represents electric charge [Only for droppers]

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

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

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

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

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Explanation

Farad is the unit of capacitance and $C = \frac{Q}{V}$ = $\frac{[Q]}{[M L^{2} T^{- 2} Q^{- 1}]}$ = $M^{- 1} L^{- 2} T^{2} Q^{2}$

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The equation of a wave is given by $Y = A \sin ω (\frac{x}{v} - k)$ where $ω$ is the angular velocity, x is length and $v$ is the linear velocity. The dimension of k is

$T^{- 1}$

T²

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Explanation

From the principle of homogenity $(\frac{x}{v})$ has dimensions of T.

$[\frac{x}{v}] = [k] [\frac{L}{L T^{- 1}}] = [k] ∴ [k] = T$

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Dimensional formula of stress is

$M^{0} L T^{- 2}$

$M^{0} L^{- 1} T^{- 2}$

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

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

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Explanation

Stress = $\frac{Force}{Area} = \frac{[M L T^{- 2}]}{[L^{2}]} = [M L^{- 1} T^{- 2}]$

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Dimensional formula of velocity of sound is

$M^{0} L T^{- 2}$

$L T^{0}$

$M^{0} L T^{- 1}$

$M^{0} L^{- 1} T^{- 1}$

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Explanation

$M^{0} L T^{- 1}$

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Dimensional formula of capacitance is

$M^{- 1} L^{- 2} T^{4} A^{2}$

$M L^{2} T^{4} A^{- 2}$

$M L T^{- 4} A^{2}$

$M^{- 1} L^{- 2} T^{- 4} A^{- 2}$

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Explanation

[C] = $(\frac{Q}{V}) = (\frac{Q^{2}}{W}) = [\frac{A^{2} T^{2}}{M L^{2} T^{- 2}}] = [M^{- 1} L^{- 2} T^{4} A^{2}]$

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$M L T^{- 1}$ represents the dimensional formula of

Power

Momentum

Force

Couple

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Explanation

Momentum = mv = $[M L T^{- 1}]$

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Dimensional formula of heat energy is

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

$M L T^{- 1}$

$M^{0} L^{0} T^{- 2}$

None of these

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Explanation

$Q = [M L^{2} T^{- 2}]$ (All energies have same dimension)

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If C and L denote capacitance and inductance respectively, then the dimensions of LC are

$M^{0} L^{0} T^{0}$

$M^{0} L^{0} T^{2}$

$M^{2} L^{0} T^{2}$

$M L T^{2}$

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Explanation

$f = \frac{1}{2 π \sqrt{L C}} \Rightarrow L C = \frac{1}{f^{2}} = [M^{0} L^{0} T^{2}]$

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Which of the following quantities has the same dimensions as that of energy

Power

Force

Momentum

Work

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Explanation

Energy = Work done [Dimensionally]

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The dimensions of "time constant" $\frac{L}{R}$ during growth and decay of current in all inductive circuit is same as that of

Constant

Resistance

Current

Time

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Explanation

$\frac{L}{R} =$ Time constant.

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