Question

The gravitational force F between two masses m and m separated by a distance r is given by F = G mâmâ/r², where G is the universal gravitational constant. What are the dimensions of G?
(A) Mâ»Â¹L³Tâ»Â²
(B) M¹L³Tâ»Â²
(C) M¹L³Tâ»Â³
(D) Mâ»Â¹L²Tâ»Â³

Answer 1

I

Explanation:

can't understand because of formula

Answer 2

Answer:

Correct answer is $G=M^{-1} L^{3} T^{-2}$

Explanation:

Since it is given that $F=\frac{GMm}{r^{2} }$

so,     $G=\frac{Fr^{2} }{Mm}$.....................(1)

For the dimension of force we know F=ma  , a=v/t  , v=d/t

a=acceleration , v=velocity, d=displacement, t=time

Dimension of velocity =$LT^{-1}$

Dimension of acceleration=$LT^{-2}$

So dimension of force $F=MLT^{-2}$...................(2)

Dimension of mass =M.........................(3)

Dimension of radius=L..........................(4)

from (1),(2),(3) and(4) we get

$G=\frac{MLT^{-2}L^{2}  }{M^{2} }$

After solving we get

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