The dimensions of universal gravitational constant are ___________.

[L^{1} M^{0} T^{0}]

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[L^{2} M^{1} T^{0}]

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[L^{- 1} M^{1} T^{- 2}]

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[L^{3} M^{- 1} T^{- 2}]

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Solution

The correct option is D $[L^{3} M^{- 1} T^{- 2}]$
$Step 1: Dimensions of standard quantities$
For mass $\to M$
For length $(r) \to L$
Force $(F) \to M L T^{- 2}$

$Step 2: Dimensions of universal gravitational constant$

From $F = \frac{G M m}{r^{2}}$

$G = \frac{F r^{2}}{M m}$

$= \frac{M L T^{- 2} [L^{2}]}{[M] [M]}$

$[G] = [M^{- 1} L^{3} T^{- 2}]$

Hence Option $D$ is correct.

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Similar questions

Q. Match List I with II and select the correct answer:

List-I	List-II
A.Spring constant	1. $M^{1} L^{2} T^{- 2}$
B.pascal	2. $M^{0} L^{0} T^{- 1}$
C.hertz	3. $M^{1} L^{0} T^{- 2}$
D.joule	4. $M^{1} L^{- 1} T^{- 2}$

Q. Match List I with List II and select the correct answer.

List - I	List - II
A) Spring constant	I) [ $M^{1} L^{2} T^{- 2}$ ]
B) Pascal	II) [ $M^{0} L^{0} T^{- 1}$ ]
C) Hertz	III)[ $M^{1} L^{0} T^{- 2}$ ]
D) Joule	IV) [ $M^{1} L^{- 1} T^{- 2}$ ]

[L^{1} M^{1} T^{- 2}]

are the dimensions of ____

Q. lf

(l_{1}, m_{1}, n_{1})

(l_{2}, m_{2}, n_{2})

(l_{3}, m_{3}, n_{3})

are the d.c.s of three mutually perpendicular lines, then the direction cosines of the line whose direction ratios are

l_{1} + l_{2} + l_{3}, m_{1} + m_{2} + m_{3}, n_{1} + n_{2} + n_{3}

are

Let L₁ and L₂ be two non-vertical lines with slopes m₁ and m₂ respectively. If α₁ and α₂ are the inclinations of lines L₁ and L₂, respectively. the acute angle (say θ) between lines L1 and L2 , is given by

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The dimensions of universal gravitational constant are ___________.

The correct option is D [L3M−1T−2]Step 1: Dimensions of standard quantities For mass →M For length (r)→L Force (F)→MLT−2Step 2: Dimensions of universal gravitational constant From F=GMmr2 G=Fr2Mm =MLT−2[L2][M][M] [G]=[M−1L3T−2]Hence Option D is correct.