Question

The radius of earth is 6370Km and of mars is 3400 Km. If an object weighs 200N or earth, what will be its weight on mars. The mass of mars is 0.11 that of earth.

Answer 1

Answer:

The weight of the object on the mars = 77.22 N.

Explanation:

The weight of an object on the Earth is given by

$\rm W = \dfrac{GM_em}{R_e^2}......\ (1).$

where,

• G = Universal Gravitational constant.
• $\rm M_e$ = mass of the Earth.
• $\rm m$ = mass of the object.
• $\rm R_e$ = radius of the Earth.

Given that,

• $\rm R_e = 6370\ km.$
• $\rm W = 200\ N.$
• Radius of the mars, $\rm R_m = 3400\ km.$
• Mass of the mars, $\rm M_m = 0.11\times M_e.$

The weight of the same object on the mars is given by

$\rm W_m = \dfrac{GM_mm_m}{R_m^2}=\dfrac{G(0.11\times M_e)m}{R_m^2}\ ......\ (2).$

Dividing equation (1) by (2), we get,

$\rm \dfrac{W}{W_m}=\dfrac{\dfrac{GM_em}{R_e^2}}{\dfrac{G(0.11\times M _e)m}{R_m^2}}=\dfrac{R_m^2}{0.11R_e^2}\\\\W_m = W\times \dfrac{0.11\times R_e^2}{R_m^2}=200\ N\times\dfrac{0.11\times (6370\ km)^2}{(3400\ km) ^2} =77.22\ N.$