The acceleration due to gravity on the surface of mercury is [tex]\boxed{3.697\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^{\text{2}}}}}} \right. \kern-\nulldelimiterspace} {{{\text{s}}^{\text{2}}}}}}[/tex].
Further Explanation:
Given:
The mass of the planet Mercury is [tex]3.30 \times {10^{23}}\,{\text{kg}}[/tex].
The radius of the planet Mercury is [tex]2.44 \times {10^6}\,{\text{m}}[/tex].
Concept:
The gravitational force of attraction experienced by a body due to another body is directly proportional to the product of their masses and inversely proportional to the square of the distance between the two bodies.
According to the Newton’s law of Gravitation, the force experienced by the body under the gravity is expressed as:
[tex]\begin{aligned}mg&=\frac{{GMm}}{{{R^2}}}\\g&=\frac{{GM}}{{{R^2}}}\\\end{aligned}[/tex]
Here, [tex]M[/tex] is the mass of the planet mercury, [tex]g[/tex] is the acceleration due to gravity on the surface of mercury, [tex]G[/tex] is the gravitational constant and [tex]R[/tex] is the radius of the planet.
The value of the Gravitational constant is [tex]6.67 \times {10^{ - 11}}\,{{{\text{N}} \cdot {{\text{m}}^{\text{2}}}} \mathord{\left/ {\vphantom {{{\text{N}} \cdot {{\text{m}}^{\text{2}}}} {{\text{k}}{{\text{g}}^{\text{2}}}}}} \right. \kern-\nulldelimiterspace} {{\text{k}}{{\text{g}}^{\text{2}}}}}[/tex].
Substitute the values of gravitational constant, mass of the planet and radius of the planet in above expression.
[tex]\begin{aligned}g&=\frac{{\left({6.67 \times{{10}^{-11}}}\right)\times\left({3.30\times{{10}^{23}}}\right)}}{{{{\left({2.44\times{{10}^6}}\right)}^2}}}\\&= \frac{{2.20 \times {{10}^{13}}}}{{5.95 \times {{10}^{12}}}}\\&=3.697\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace} {{{\text{s}}^{\text{2}}}}}\\\end{aligned}[/tex]
Thus, the acceleration due to gravity on the surface of mercury is [tex]\boxed{3.697\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^{\text{2}}}}}} \right. \kern-\nulldelimiterspace} {{{\text{s}}^{\text{2}}}}}}[/tex].
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Gravitation
Keywords:
Mercury, acceleration due to gravity on Mercury, radius, 2.44x10^6 m, 3.30x10^23 kg, Newton’s law, gravitation, Gravitational constant, F=GMm/r^2.
