Question

The unit of gravitational field is
A $\dfrac{N}{{kg}}$
B $\dfrac{N}{s}$
C $\dfrac{{kg}}{{{s^2}}}$
D $\dfrac{N}{{kg{m^2}}}$

Answer 1

Hint
As we know that gravitational field = gravitational force/mass
So the unit of gravitational field = unit of gravitational force/ unit of mass
The unit of gravitational force = N
Unit of mass = kg

Complete step-by-step answer:
Gravitational field due to any object is defined as the gravitational force on any unit mass due to that object at that point.
According to Newton’s gravitational law of motion, the gravitational force between two objects of mass M and m separated by a distance r is
$F = \dfrac{{GMm}}{{{r^2}}}$where, G is universal gravitational constant
If we put m=1 then we will get gravitational field due to an object of mass M at a distance r is
$E = \dfrac{{GM}}{{{r^2}}}$
So gravitational field = gravitational force/mass
Therefore, unit of gravitational field = unit of gravitational force/ unit of mass
Now, gravitational force has the same unit of force so it’s unit N (newton)
And the unit of mass is kg
So the unit of gravitational field is $\dfrac{N}{{kg}}$
Hence, option (A) is correct.

Note
As the gravitational force between two objects of mass M and m separated by the distance r is $F = \dfrac{{GMm}}{{{r^2}}}$and gravitational field is $E = \dfrac{{GM}}{{{r^2}}}$. Gravitational field is used to explain the influence of an object around it. We can state that whenever the object comes under the influence of the object it can feel the gravitational force due to the presence of the gravitational field due to other objects.