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Model Paper 8 — Science STD 9 — Question

Gujarat BoardEnglish MediumSTD 9ScienceModel Paper 85 Marks
Question
Define acceleration due to gravity. Derive an expression for acceleration due to gravity in terms of mass of the earth (M) and universal gravitational constant (G).
✓

Answer

Acceleration due to gravity: The acceleration produced in the motion of a body falling under the force of gravity is called acceleration due to gravity. It is denoted by ' g '. It is expressed in units, $ms ^{-2}$.
Expression for acceleration due to gravity: The force ( F ) of gravitational attraction on a body of mass $m$ due to earth of mass M and radius R is given by, $F = G \frac{ mM }{ R ^2}$........(1)
Where, 'G' is universal gravitational constant.
According to Newton's second law of motion: Force is the product of mass and acceleration.
$
\therefore F=m a
$
But the acceleration due to gravity is represented by the symbol g .
Therefore, we can write; F = mg  $\qquad.....(2)$
From equation (1) and (2), we get
$
mg=G \frac{m M}{R^2} \text { or } g=\frac{G M}{R^2} \ldots \text { (3) }
$
When the body is at a distance ' R ' from centre of the earth then $g =\frac{G M}{R^2}$.
It may be noted that, value of ' g ' is independent of mass of object.

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