Question

Please answer the question for gravitational field attached in the image.

Answer 1

We are given:

Radius of Venus=  6 * 10⁶ m

Height above the planet's ground = 9.4 * 10⁶ m

Mass of Venus = 4.867 * 10²⁴ kg

Finding the Gravitational Field:

We first need to calculate the distance between the center of masses

Distance between center of masses:

Since the point is above the surface of Venus, the radius of Venus and the height will add

Distance between the center of masses = 9.4*10⁶ + 6 * 10⁶

Distance (r) = 15.4 * 10⁶ m

Now back to Gravitational field!

We know the formula for Gravitational Field:

g = GM / r² [where g is the gravitational field, M is the mass of the planet, r is the distance between the center of masses and G is the gravitational constant]

plugging the known values in the formula:

g = (6.67 * 10⁻¹¹ * 4.867 * 10²⁴) / (15.4*10⁶)²       [G = 6.67*10⁻¹¹ Nm²/kg²]

g = (32.46 * 10¹³) / (237 * 10¹²)

g = (32.46 * 10¹³) / (23.7 * 10¹³)

g = 32.46/23.7                                                   [the 10¹³ got cancelled out]

g = 1.367 N/kg² (or m/s²)