A body weights \(700 \mathrm{~g} \mathrm{wt}\) on the surface of earth. How much it weight on the surface of planet whose mass is \(1 / 7\) and radius is half that of the earth (A) \(200 \mathrm{~g} \mathrm{wt}\) (B) \(400 \mathrm{~g} \mathrm{wt}\) (C) \(50 \mathrm{~g} \mathrm{wt}\) (D) \(300 \mathrm{~g}\) wt.

Knowing the mass and radius of the new planet, calculate the acceleration due to gravity using the formula: \(g_{planet} = G \cdot \frac{M_{planet}}{R_{planet}^2}\) where - \(g_{planet}\) is the acceleration due to gravity on the surface of the new planet, - G is the gravitational constant \((6.674 \times 10^{-11}\,m^3⋅kg^{−1}⋅s^{−2})\), - \(M_{planet}\) is the mass of the new planet, and - \(R_{planet}\) is the radius of the new planet. Considering the mass of the planet is 1/7 that of Earth \((5.972 × 10^24 kg)\) and the radius is half that of Earth \((6.371 × 10^6 m)\), we have: \(M_{planet} = 5.972 \times 10^{24} \cdot(\frac{1}{7}) kg\) \(R_{planet} = 6.371 \times 10^{6} \cdot (\frac{1}{2}) m\) Then, calculate \(g_{planet}\) using the above formula.

The mass given is in grams, so we need to convert it to kilograms to match the units in the rest of the calculations: \(m_{body\_kg} = \frac{700 \; g}{1000} = 0.7 \; kg\)

Now we can find the new weight (gravitational force) of the body on the surface of the new planet using the formula: \(F_{planet} = m_{body\_kg} \cdot g_{planet}\) where - \(F_{planet}\) is the new weight of the body on the surface of the new planet, - \(m_{body\_kg}\) is the mass of the body in kg, and - \(g_{planet}\) is the acceleration due to gravity on the surface of the new planet (found in Step 1). Calculate \(F_{planet}\) using the values obtained in Step 1 and Step 2.

Finally, convert the new weight of the body from kilograms to grams to compare with the given choices: \(F_{planet\_grams} = F_{planet} \cdot 1000 \) Compare \(F_{planet\_grams}\) with the given choices (A, B, C, and D) to determine the correct answer.