Conversion of 1 MW power in a new system having basic unit of mass, length and time as 10 kg , 1 dm

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1.Units, Dimensions and Measurement

medium

The conversion of $1 \;MW$ power in a new system having basic unit of mass, length and time as $10 \;kg , 1 \;dm$ and $1 \;minute$ respectively is:

A$2.16 \times {10^{12}}unit$

B$1.26 \times {10^{12}}unit$

C$2.16 \times {10^{10}}unit$

D$2 \times {10^{14}}unit$

Solution

$[P] = [M{L^2}{T^{ – 3}}]$
${n_2} = {n_1}{\left[ {\frac{{{M_1}}}{{{M_2}}}} \right]^x}\,{\left[ {\frac{{{L_1}}}{{{L_2}}}} \right]^y}\,{\left[ {\frac{{{T_1}}}{{{T_2}}}} \right]^z}$$ = 1 \times {10^6}\,{\left[ {\frac{{1\,kg}}{{10\,kg}}} \right]^1}\,{\left[ {\frac{{1m}}{{1\,dm}}} \right]^2}\,{\left[ {\frac{{1s}}{{1\min }}} \right]^{ – 3}}$ [$\,1MW = {10^6}W$]
$ = {10^6}\left[ {\frac{{1kg}}{{10kg}}} \right]\,{\left[ {\frac{{10\,dm}}{{1\,dm}}} \right]^2}\,{\left[ {\frac{{1sec}}{{60sec}}} \right]^{ – 3}}$$ = 2.16 \times {10^{12}}$unit

Standard 11

Physics

The equation $\frac{{dV}}{{dt}} = At – BV$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are

medium

The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are

medium

(AIPMT-1990)

The volume of a liquid flowing out per second of a pipe of length $l$ and radius $r$ is written by a student as $V\, = \,\frac{{\pi p{r^4}}}{{8\eta l}}$ where $p$ is the pressure difference between the two ends of the pipe and $\eta $ is coefficent of viscosity of the liquid having dimensional formula $[M^1L^{-1}T^{-1}] $. Check whether the equation is dimensionally correct.

medium

Match the following two coloumns

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

medium

If $\varepsilon_0$ is permittivity of free space, $e$ is charge of proton, $G$ is universal gravitational constant and $m_p$ is mass of a proton then the dimensional formula for $\frac{e^2}{4 \pi \varepsilon_0 G m_p{ }^2}$ is

medium

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 conversion of $1 \;MW$ power in a new system having basic unit of mass, length and time as $10 \;kg , 1 \;dm$ and $1 \;minute$ respectively is:

Solution

Similar Questions

The equation $\frac{{dV}}{{dt}} = At – BV$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are

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If $\varepsilon_0$ is permittivity of free space, $e$ is charge of proton, $G$ is universal gravitational constant and $m_p$ is mass of a proton then the dimensional formula for $\frac{e^2}{4 \pi \varepsilon_0 G m_p{ }^2}$ is

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