If the buoyant force $F$ acting on an object depends on its volume $V$ immersed in a liquid, the density $\rho$ of the liquid and the acceleration due to gravity $g$. The correct expression for $F$ can be
If the buoyant force $F$ acting on an object depends on its volume $V$ immersed in a liquid, the density $\rho$ of the liquid and the acceleration due to gravity $g$. The correct expression for $F$ can be
- A
$V \rho g$
- B
$\frac{\rho g}{V}$
- C
$\rho g V^2$
- D
$\sqrt{\rho g V}$
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What is dimensional analysis ? Write limitation of dimensional analysis.
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The equation of a wave is given by$Y = A\sin \omega \left( {\frac{x}{v} - k} \right)$where $\omega $ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is
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$(a)$ $K=m^{2} v^{3}$
$(b)$ $K=(1 / 2) m v^{2}$
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$(d)$ $K=(3 / 16) m v^{2}$
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The $SI$ unit of energy is $J=k g\, m^{2} \,s^{-2} ;$ that of speed $v$ is $m s^{-1}$ and of acceleration $a$ is $m s ^{-2} .$ Which of the formulae for kinetic energy $(K)$ given below can you rule out on the basis of dimensional arguments ( $m$ stands for the mass of the body ):
$(a)$ $K=m^{2} v^{3}$
$(b)$ $K=(1 / 2) m v^{2}$
$(c)$ $K=m a$
$(d)$ $K=(3 / 16) m v^{2}$
$(e)$ $K=(1 / 2) m v^{2}+m a$
The Bernoulli's equation is given by $p +\frac{1}{2} \rho v ^{2}+ h \rho g = k$
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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