The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are

  • [KVPY 2020]
  • A

    $ - \frac{3}{2},\,\frac{1}{2},\,1$

  • B

    $ - 1,\, - 2,\,3$

  • C

    $\frac{1}{2},\, - \frac{3}{2},\, - \frac{1}{2}$

  • D

    $1,\,2,\,\frac{1}{3}$

Similar Questions

If the units of force, energy and velocity are respectively $10\, N, 100\, J, 5\, m/s$, then  the units of length, mass and time will be

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 

It is estimated that per minute each $cm^2$ of earth receives about $2\ cal (1\ cal = 4.18\ J)$ of heat energy from the sun. This is called Solar constant. In $SI$ units the value is :-

The amount of heat energy $Q$, used to heat up a substance depends on its mass $m$, its specific heat capacity $(s)$ and the change in temperature $\Delta T$ of the substance. Using dimensional method, find the expression for $s$ is (Given that $\left.[s]=\left[ L ^2 T ^{-2} K ^{-1}\right]\right)$ is

If velocity$(V)$, force$(F)$ and time$(T)$ are chosen as fundamental quantities then dimensions of energy are