Question

Planet A has double the radius than that of planet B. If the mass of planet A is 4 times heavier than the mass of planet B, then which of the following statements regarding weight of an object is correct?

(a) Heavier on planet A than on planet B.

(b) Heavier on planet B than on planet A.

(c) Same on both the planets.

(d) Cannot be measured on planet B.

Answer 1

Correct option is (c) Same on both the planets.

Let mass of the object is m, weight of the object on planet A is

\(w_A = \frac{GM_Am}{R_A^2}\)

where, M_A and R_A are mass and radius of planet A, respectively.

Similarly, weight on planet B is

\(w_B = \frac{GM_Bm}{R_B^2}\)

\(\therefore \frac{w_A}{w_B} = \frac{M_A}{M_B} \times \left(\frac{R_B}{R_A}\right)^2\)

\(= 4 \times (\frac 12)^2 \)

\(=1\)

⇒ \(w_A = w_B\)    \((\therefore M_A = 4 M_B \text{ and } R_A = 2R_B)\)