Force (F) and density (d) are related as F, = ,frac{α }{{β , + ,√ d }} then dimension of ?

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1.Units, Dimensions and Measurement

medium

Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ and $\beta$ are

A$M^{3/2} L^{-1/2} T^{-2}, M^{1/2} L^{-3/2} T^0$

B$M^{1/2 }L^{-3/2} T^{-2}, M^{-3/2} L^{-3/2} T^0$

C$M^{3} L^{-1} T^{-2/3}, M^{2} L^{-3} T^{2}$

D$M^{2} L^{-1/2} T^{-2}, M^{3/2} L^{-1/2} T^0$

Solution

$\alpha = \,\,\left[ {F\sqrt d } \right]\,\, = \,\,\left[ {ML{T^{ – 2}}} \right]\,\left[ {{M^{1/2}}\,{L^{ – 3/2}}} \right]\,\, = \,\,{M^{3/2}}{L^{ – 1/2}}{T^{ – 2}},\,$
$\,\left[ \beta \right]\,\, = \,\,{\left[ d \right]^{1/2}}\,\, = \,\,{\left[ {{M^1}{L^{ – 3}}\,{T^0}} \right]^{1/2}}\,\, = \,\,\left[ {{M^{1/2}}\,{L^{ – 3/2}}{T^0}} \right]$

Standard 11

Physics

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medium

(JEE MAIN-2023)

Consider the following equation of Bernouilli’s theorem. $P + \frac{1}{2}\rho {V^2} + \rho gh = K$ (constant)The dimensions of $K/P$ are same as that of which of the following

easy

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medium

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

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medium

Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ and $\beta$ are

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