The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$, its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,
The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$, its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,
- [KVPY 2015]
- A
$\alpha=-2, \beta=-2$ and $\gamma=4$
- B
$\alpha=2, \beta=2$ and $\gamma=-4$
- C
$\alpha=3, \beta=3$ and $\gamma=-2$
- D
$\alpha=-3, \beta=-3$ and $\gamma=2$
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If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} $ . It is observed that the time period is directly proportional to $\sqrt {\frac{d}{s}} $ . The value of $b$ should therefore be
If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} $ . It is observed that the time period is directly proportional to $\sqrt {\frac{d}{s}} $ . The value of $b$ should therefore be
- [JEE MAIN 2013]
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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
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- [AIIMS 1985]
Dimensions of potential energy are
Dimensions of potential energy are