The dimensions of universal gravitational constant are

  • [AIIMS 2000]
  • [AIPMT 1992]
  • [AIPMT 2004]
  • A

    ${M^{ - 2}}{L^2}{T^{ - 2}}$

  • B

    ${M^{ - 1}}{L^3}{T^{ - 2}}$

  • C

    $M{L^{ - 1}}{T^{ - 2}}$

  • D

    $M{L^2}{T^{ - 2}}$

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  • [IIT 1983]

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: [position $]=\left[X^\alpha\right] ;[$ speed $]=\left[X^\beta\right]$; [acceleration $]=\left[X^{ p }\right]$; [linear momentum $]=\left[X^{ q }\right]$; [force $]=\left[X^{ I }\right]$. Then -

$(A)$ $\alpha+p=2 \beta$

$(B)$ $p+q-r=\beta$

$(C)$ $p-q+r=\alpha$

$(D)$ $p+q+r=\beta$

  • [IIT 2020]

Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P .$ The viscosity of oil is given by $\eta=\frac{P\left(r^{2}-x^{2}\right)}{4 v l}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are

  • [AIPMT 1993]