What are the units of $K=1\text{​}/\text{​}4\pi {\epsilon }_{0}$

(1) C2N–1m–2

(2) Nm2C–2

(3) Nm2C2

(4) Unitless

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The SI unit of surface tension is

(1) Dyne/cm

(2) Newton/cm

(3) Newton/metre

(4) Newton-metre

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E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{E{l}^{2}}{{m}^{5}{G}^{2}}$ are

(1) Angle

(2) Length

(3) Mass

(4) Time

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From the equation $\mathrm{tan}\theta =\frac{rg}{{v}^{2}}$, one can obtain the angle of banking θ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is

(1) Both dimensionally and numerically correct

(2) Neither numerically nor dimensionally correct

(3) Dimensionally correct only

(4) Numerically correct only

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A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity η flowing per second through a tube of radius r and length l and having a pressure difference p across its end, is

(1) $V=\frac{\pi p{r}^{4}}{8\eta l}$

(2) $V=\frac{\pi \eta l}{8p{r}^{4}}$

(3) $V=\frac{8p\eta l}{\pi {r}^{4}}$

(4) $V=\frac{\pi p\eta }{8l{r}^{4}}$

Concept Questions :-

Dimensions
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The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation $v=at+\frac{b}{t+c}$; the dimensions of a, b and c are

(1) $a={L}^{2},\text{\hspace{0.17em}}b=T,\text{\hspace{0.17em}}c=L{T}^{2}$

(2) $a=L{T}^{2},\text{\hspace{0.17em}}b=LT,\text{\hspace{0.17em}}c=L$

(3) $a=L{T}^{-2},b=L,\text{\hspace{0.17em}}c=T$

(4) $a=L,\text{\hspace{0.17em}}b=LT,\text{\hspace{0.17em}}c={T}^{2}$

Concept Questions :-

Dimensions
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From the dimensional consideration, which of the following equation is correct ?

(1) $T=2\pi \sqrt{\frac{{R}^{3}}{GM}}$

(2) $T=2\pi \sqrt{\frac{GM}{{R}^{3}}}$

(3) $T=2\pi \sqrt{\frac{GM}{{R}^{2}}}$

(4) $T=2\pi \sqrt{\frac{{R}^{2}}{GM}}$

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The position of a particle at time t is given by the relation  , where v0 is a constant and α > 0. The dimensions of v0 and α are respectively

(1) ${M}^{0}{L}^{1}{T}^{-1}$ and T–1

(2) ${M}^{0}{L}^{1}{T}^{0}$ and T–1

(3) ${M}^{0}{L}^{1}{T}^{-1}$ and LT–2

(4) ${M}^{0}{L}^{1}{T}^{-1}$ and T

Concept Questions :-

Dimensions
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The dimensions of $\frac{a}{b}$ in the equation $P=\frac{a-{t}^{2}}{bx}$, where P is pressure, x is distance and t is time, are

(1) MT–2

(2) M2LT–3

(3) ML3T–1

(4) LT–3

Concept Questions :-

Dimensions
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Dimensions of $\frac{1}{{\mu }_{0}{\epsilon }_{0}}$, where symbols have their usual meaning, are

(1) [LT–1]

(2) [L–1T]

(3) [L–2T2]

(4) [L2T–2]

Concept Questions :-

Dimensions
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