Question

Calculate the force of gravitation due to earth on a ball of mass 60kg.

Answer 1

Hint: Calculate the distance between the center of the earth and the ball to find out the force of gravitation. For this purpose, we used the gravitational formula. And we have to know the value of the universal gravitational constant, it has a very small value. The unit of force is Newton, denoted by N.
Formula used:
$F=\dfrac{GMm}{{{r}^{2}}}$

Complete step-by-step solution
Given,
Universal gravitational constant (G )= $6.7\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}}$
Mass of earth (M) = $6\times {{10}^{24}}kg$
Mass of the ball: 60kg
Distance between center earth and ball r = Radius of earth
$6.4\times {{10}^{3}}km$
$\Rightarrow $$6.4\times {{10}^{3}}\times 1000m$
$\Rightarrow $$6.4\times {{10}^{6}}m$
Force of gravitation $F=\dfrac{GMm}{{{r}^{2}}}$
Now, putting these values in the above mentioned formula we get
$=\dfrac{6.7\times {{10}^{-11}}\times 6\times {{10}^{24}}\times 60}{{{\left( 6.4\times {{10}^{6}} \right)}^{2}}}$
$=\dfrac{6.7\times 6\times 60\times {{10}^{-11}}\times {{10}^{24}}}{6.4\times 6.4\times {{10}^{12}}}$
$\Rightarrow $58.88$\times $10
$\therefore $ 588.8N
Additional information:
i). Force of gravitation is an attractive force.
ii). Gravitational force is independent of medium (air, water, etc).
iii). The force acting on a body is equal and opposite, and remember this formula is valid for point masses.
iv). The unit of Universal gravitational constant ‘G ‘is $N{{m}^{2}}/k{{g}^{2}}$. Many times questions appeared on this unit in the JEE examination.
v). This formula arises from Newton’s law of gravitation.
vi). The force of gravitational is inversely proportional to the square of the distance between the given two bodies.
vii). In some numerical, we have to remember a very basic thing is the mass can be written as a product of density and volume of the given body (m= $\rho $× v ).

Note: Instead of this formula we can used
$F=ma$
$\Rightarrow $F=mg formula.
Similarly, this question may ask through a little bit of change in mass maybe 1kg or 2kg of the ball. Like this, we can practice this question to solve.