What is the force of gravity between the earth and mass 1 kg placed on its surface?

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Solution

Step 1: Given informationMass of object, m1=1kg.Mass of earth, m2=6×1024kgRadius of earth, R =6.4×106mStep 2: Write an expression for the magnitude of gravitational force as follows:F=Gm1m2R2Here, Gis the gravitational constant.Substitute 1kg for m1, 6×1024kg for m2, 6.4×106m for R and 6.67×10-11Nm2kg2 for G in expression of gravitational forceF= 6.67×10-11Nm2kg2×1kg×6×1024kg6.4× 106m2=9.8NHence, magnitude of the gravitational force is 9.8N.

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Solution

Mass of the body, m= 1 kg Mass of the Earth, M= 6 x 10^24 kg Radius of the earth, R= 6.4 x 10^6 m Now magnitude of the gravitational force (F) between the earth and the body can be given as F = GMm/R^2. Putting values we get, F = 9.8 N

Answer

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Hint: Use the equation for force of gravity acting on the object. Mass of the object is given in the question and we know the value for g i.e. acceleration due to gravity. Substitute these values in the equation for force of gravity directly and calculate the force of gravity between the earth and mass placed on its surface.

Complete answer:
Given: Mass (m)= 20 kg
The equation for force of gravity acting on the object near the surface of the earth is given by,
$F=mg$ …(1)
Where, m is the mass
               g is the acceleration due to gravity
Substituting values in the equation. (1) we get,
$F = 20 \times 9.8$
$\therefore F= 196 N$
Hence, the force of gravity between the earth and mass placed on its surface is 196 N.

Additional Information:
Acceleration due to gravity around the surface is approximately $9.8 {m}/{{s}^{2}}$. As the height from the Earth increases, the acceleration due to gravity changes. As the height increases, acceleration due to gravity decreases. Similarly, as the depth decreases, gravity inside the earth decreases.

Note:
According to Newton’s law of universal gravitation, every mass experiences attractive force due to which they are bound together. This attractive force is experienced by every mass irrespective of its size and it even influences everything. Gravitational force is an attractive force.
Students need to note that the gravitational force or force of gravity between the objects is inversely proportional to the square of the distance between them. As the distance between the objects vary, the attractive force between the objects also vary by multiple factors.

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