The units of G must be C. m³ / ( kg s² )
Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:
[tex]\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }[/tex]
F = Gravitational Force ( Newton )
G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )
m = Object's Mass ( kg )
R = Distance Between Objects ( m )
Let us now tackle the problem !
To find unit of Gravitational Constant can be carried out in the following way:
[tex]F = G \frac{m_1 ~ m_2}{R^2}[/tex]
[tex]{[N]}= G\frac{{[kg]}{[kg]}}{{[m^2]}}[/tex]
[tex]{[kg ~ m / s^2]}= G \frac{{[kg^2]}}{{[m^2]}}[/tex]
[tex]G = \frac{{[kg ~ m / s^2]}{[m^2]}} {{[kg^2]} }[/tex]
[tex]G = \frac{{[kg ~ m^3 / s^2]}} {{[kg^2]} }[/tex]
[tex]G = \frac{{[m^3 / s^2]}} {{[kg]} }[/tex]
[tex]\boxed {G = \frac{{[m^3]}} {{[kg ~ s^2]} }}[/tex]
The unit of G must be [tex]\large {\boxed {\frac{m^3} {kg ~ s^2 }}}[/tex]
Grade: High School
Subject: Physics
Chapter: Gravitational Fields
Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
The unit of the gravitational constant is [tex]\boxed{{{{{\text{m}}^{\text{3}}}} \mathord{\left/{\vphantom {{{{\text{m}}^{\text{3}}}} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}} \right.\kern-\nulldelimiterspace} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}}[/tex].
Further Explanation:
The Newton’s law of gravitation states that the force of attraction experienced by two bodies is directly proportional to the product of their mass and inversely proportional to the square of the distance between the two bodies.
The mathematical expression for the Newton’s law of gravitation is as shown below.
[tex]F = \dfrac{{G{m_1}{m_2}}}{{{r^2}}}[/tex]
Here, [tex]G[/tex] is the gravitational constant, [tex]{m_1}\& {m_2}[/tex] are the mass of two bodies and [tex]r[/tex] is the distance of the bodies.
Simplify the expression for the gravitational constant [tex]G[/tex].
[tex]G = \dfrac{{F{r^2}}}{{{m_1}{m_2}}}[/tex]
The SI unit of force is [tex]{{{\text{kg}} \cdot {\text{m}}} \mathord{\left/{\vphantom {{{\text{kg}} \cdot {\text{m}}} {{{\text{s}}^{\text{2}}}}}} \right.\kern-\nulldelimiterspace} {{{\text{s}}^{\text{2}}}}}[/tex], the unit of distance is and the unit of mass is [tex]{\text{kg}}[/tex].
Substitute the SI units of force, distance and mass in the above expression.
[tex]\begin{aligned}G&=\dfrac{(\text{kg}\cdot\text{m/s}^2)(\text{m})^2}{(\text{kg})(\text{kg})}\\&=\frac{\text{m}^2}{\text{kg}\cdot\text{s}^2}\\&=\text{m}^3/\text{kg}\cdot\text{s}^2\end{aligned}[/tex]
Thus, the unit of the gravitational constant is [tex]\boxed{{{{{\text{m}}^{\text{3}}}} \mathord{\left/{\vphantom {{{{\text{m}}^{\text{3}}}} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}} \right.\kern-\nulldelimiterspace} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}}[/tex].
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Answer Details:
Grade: High School
Chapter: Gravitation
Subject: Physics
Keywords: Gravity, attracts, SI units, two bodies, one another, force, masses of the body, magnitude of force, gravitational constant, distance, units.
