If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be

  • [AIPMT 2015]
  • [AIEEE 2012]
  • A

    $[EV^{-2}T^{-1}]$

  • B

    $[EV^{-1}T^{-2}]$

  • C

    $[EV^{-2}T^{-2}]$

  • D

    $[E^{-2} V^{-1}T^{-3}]$

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$A$ and $B$ are constants. The dimensions of $AB$ are

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A massive black hole of mass $m$ and radius $R$ is spinning with angular velocity $\omega$. The power $P$ radiated by it as gravitational waves is given by $P=G c^{-5} m^{x} R^{y} \omega^{z}$, where $c$ and $G$ are speed of light in free space and the universal gravitational constant, respectively. Then,

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convert $1\; newton$ ($SI$ unit of force) into $dyne$ ($CGS$ unit of force) 

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  • [IIT 2020]

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  • [KVPY 2011]