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Given, weight on the surface of the earth,

${W_E} = 3.5kgwt$

$ = 3.5 \times 9.8$

$ = 34.3N$

Mass of the planet,${M_p} = \dfrac{{{M_E}}}{7}$

$\dfrac{{{M_P}}}{{{M_E}}} = \dfrac{1}{7}$ …………………. (1)

Radius of the planet,${R_P} = \dfrac{{{R_E}}}{2}$

$\dfrac{{{R_P}}}{{{R_E}}} = \dfrac{1}{2}$ …………………(2)

Here we need to find weight of the given body on the surface of the planet,${W_P} = ?$

Consider a mass of earth be ${M_E}$ and radius ${R_E}$. The force of attraction due to earth on a body of mass m on the surface of earth is given by,

$F = \dfrac{{G{M_E}m}}{{{R_E}^2}}$ ………………… (a)

This force produces an acceleration g during motion of a body under gravity. Then,

$F = mg$ ………………… (b)

Compare equation (a) and (b), we get

$mg = \dfrac{{G{M_E}m}}{{{R_E}^2}}$

$\therefore {g_E} = \dfrac{{G{M_E}}}{{{R^2}_E}}$ ………………… (3) this is an equation for acceleration due to gravity on the surface of earth.

We know that,${W_E} = m{g_E}$

${W_P} = m{g_P}$

Substitute equation (3) in the above equations,

${W_E} = m\left( {\dfrac{{G{M_E}}}{{{R^2}_E}}} \right)$ ………………………. (4)

Similarly, ${W_P} = m\left( {\dfrac{{G{M_P}}}{{{R^2}_P}}} \right)$ ……………………. (5)

Now divide equation ( 5) by (4) we get,

$\dfrac{{{W_P}}}{{{W_E}}} = \dfrac{{m\left( {\dfrac{{G{M_P}}}{{{R^2}_P}}} \right)}}{{m\left( {\dfrac{{G{M_E}}}{{{R^2}_E}}} \right)}}$

Simplifying the above equation we get,

$\dfrac{{{W_P}}}{{{W_E}}} = \dfrac{{{M_P}}}{{{M_E}}} \times {\left( {\dfrac{{{R_E}}}{{{R_P}}}} \right)^2}$

Now substitute equation (1) and (2),

We get, $\dfrac{{{W_P}}}{{3.5}} = \dfrac{1}{7} \times {\left( {\dfrac{2}{1}} \right)^2}$

$ = \dfrac{4}{7}$

Then, ${W_p} = \dfrac{4}{7} \times 3.5$

$ = 2kgwt$

$ = 2 \times 9.8$

$ = 19.6N$

1. Mass of an object is the same as the measure of its inertia. Greater the mass, the greater is the inertia.

2. Mass remains the same whether an object is on the earth, the moon or even in outer space. Mass of the object will not change from place to place.

3. Weight depends on its location. It has both magnitude and direction. The weight is a force acting vertically downwards.

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