If acceleration due to gravity is 10,m{s^{ - 2}} and units of length and time are changed in kilomet

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1.Units, Dimensions and Measurement

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If the acceleration due to gravity is $10\,m{s^{ - 2}}$ and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is

A$360000$

B$72000$

C$36000$

D$129600$

Solution

(d) ${n_2} = {n_1}{\left[ {\frac{{{L_1}}}{{{L_2}}}} \right]^1}{\left[ {\frac{{{T_1}}}{{{T_2}}}} \right]^{ – 2}}$$ = 10{\left[ {\frac{{meter}}{{km}}} \right]^1}{\left[ {\frac{{\sec }}{{hr}}} \right]^{ – 2}}$
${n_2} = 10{\left[ {\frac{m}{{{{10}^3}m}}} \right]^1}{\left[ {\frac{{\sec }}{{3600\sec }}} \right]^{ – 2}}$$ = 129600$

Standard 11

Physics

The Bernoulli's equation is given by $p +\frac{1}{2} \rho v ^{2}+ h \rho g = k$

where $p =$ pressure, $\rho =$ density, $v =$ speed, $h =$ height of the liquid column, $g=$ acceleration due to gravity and $k$ is constant. The dimensional formula for $k$ is same as that for

medium

The entropy of any system is given by

${S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]$

Where $\alpha$ and $\beta$ are the constants. $\mu, J, K$ and $R$ are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant repectively. [Take ${S}=\frac{{dQ}}{{T}}$ ]

Choose the incorrect option from the following:

hard

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If force $(F)$, velocity $(V)$ and time $(T)$ are considered as fundamental physical quantity, then dimensional formula of density will be:

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In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is

medium

If the acceleration due to gravity is $10\,m{s^{ - 2}}$ and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is

Solution

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The Bernoulli's equation is given by $p +\frac{1}{2} \rho v ^{2}+ h \rho g = k$ where $p =$ pressure, $\rho =$ density, $v =$ speed, $h =$ height of the liquid column, $g=$ acceleration due to gravity and $k$ is constant. The dimensional formula for $k$ is same as that for

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The Bernoulli's equation is given by $p +\frac{1}{2} \rho v ^{2}+ h \rho g = k$

where $p =$ pressure, $\rho =$ density, $v =$ speed, $h =$ height of the liquid column, $g=$ acceleration due to gravity and $k$ is constant. The dimensional formula for $k$ is same as that for