Question

Maximum weight of the body is
A.) At the center of the earth
B.) Inside the earth
C.) On the surface of the earth
D.) Above the surface of the earth

Answer 1

HINT : These basic questions can be answered if you remember the basics of gravitational force and also use the gravitational force formula .i.e. $g = \dfrac{{GM}}{{{r^2}}}$to find the correct option.

Complete step-by-step answer:
Let’s first discuss about weight and mass how they differ from each other;

We know that mass is a calculation of the quantity of matter that comprises it, thus Weight is the measure of the force of gravity on an object. Mass is calculated by adding a specified quantity of matter to an uncertain amount of matter using a scale. Weight is determined on a meter.

Since we know that gravity at the center is 0 and as we deeper in the earth the weaker the gravitational force gets \[g = \dfrac{4}{3}G\rho \pi r\] here we know that the g is directly proportional to the distance of object from earth. Also when distance of object from earth is increases the gravitational force decreases as we know that gravitational at height h is given as \[{g_h} = g{\left( {\dfrac{{1 + h}}{R}} \right)^2}\]here he is the height of the object from earth and R is radius of the earth.

For the object at surface gravitational force will be maximum and it is given by $g = \dfrac{{GM}}{{{r^2}}}$here r is the radius of the earth.

Therefore the weight of the body will be maximum at the surface of the earth.

Note: Here we have found that gravity is the fundamental basis of this problem, which can be explained as Gravity is the force by which the earth draws the body to its center. Let's find two ${m_a}$ and ${m_b}$ mass corps. The mass in terms of mass is given by the application of equal forces on two bodies by: ${m_b} = {m_a}\left[ {\dfrac{{aA}}{{aB}}} \right]$this is called an inertial mass of a body. Under the influence of gravity on two bodies, mass is given by ${F_A} = \dfrac{{GM{m_A}}}{{{r^2}}}$ and ${F_B} = \dfrac{{GM{m_B}}}{{{r^2}}}$.