Question

which of the following is not the unit of universal gravitational constant 'G'​

Answer 1

Answer:

The correct answer is option 4) i.e. m2 s2 N-1

CONCEPT:

Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

Dimensional formula of gravitational constant:

We know,

⇒ G =

Dimensional formula of force, F = mass × acceleration ⇒ M1 L1T-2

∴ G = M-1L3T-2

EXPLANATION:

On comparing the given options with the dimensional formula of G:

m3 kg-1 s2 ⇒ M-1L3T-2

N m2 kg-2 ⇒ (unit of force) m2 kg-2 ⇒ [M1 L1T-2 ] [L2] [M-2] ⇒ M-1L3T-2

dyne cm2 g-2 ⇒ (unit of force) cm2 g-2 ⇒ [M1 L1T-2] [L2] [M-2] ⇒ M-1L3T-2

m2 s2 N-1 ⇒ m2 s2 (unit of force)-1 ⇒ [M2] [T2] [M1 L1T-2] ⇒ M3L1T0

Therefore, m2 s2 N-1 is not the unit of gravitational constant.