Question

The mass Of jupiter is 1.9 x 10^27kg and its radius is 71*10^6 m Calulate the acceleration due to gravity of jupiter and also the weight Of a person having mass 800kg.​

Answer 1

Given

• Mass of Jupiter, M = 1.9 × 10²⁷ kg
• Radius of Jupiter, R = 71 × 10⁶ m
• Universal Gravitational constant, G = 6.67 × 10⁻¹¹ Nm²kg⁻²
• Mass of person on Jupiter's surface, m = 800 kg

To find

• Acceleration due to gravity on jupiter's surface, g =?
• Weight of person with 800 kg mass, W =?

Formulae required

• Formula for acceleration due to gravity

        g = GM / R²

• Formula for weight of body

        W = mg

[ Where g is acceleration due to gravity, G is universal gravitational constant, M is mass of specific celestial body, R is the distance between centre and surface of celestial body, W is the weight of body of mass m on Jupiter's surface]

Solution

Calculating the acceleration due to gravity of jupiter Using formula

→ g = GM / R²

→ g = (6.67 × 10⁻¹¹ Nm²kg⁻²) (1.9 × 10²⁷ kg) / (71 × 10⁶ m)²

→ g = 0.00251 × 10⁴

→ g = 25.1 m/s²

Now,

Calculating the weight of person with mass 800 kg

→ W = mg

→ W = 800 × 25.1

→ W = 20080 N

Therefore,

• Acceleration due to gravity of jupiter is 25.1 m/s², and
• Weight of the person is be 20080 N.

Answer 2

Answer:

Given :-

• The mass of Jupiter is 1.9 × 10²⁷ and it's radius is 71 × 10⁶ and mass is 800 kg.

To Find :-

• What is the acceleration due to gravity of jupiter and weight of a person.

Formula Used :-

❶ To find acceleration due to gravity we know that,

${\purple{\boxed{\large{\bold{g =\: \dfrac{GM}{{r}^{2}}}}}}}$

where,

• g = Acceleration due to gravity
• G = Gravitational constant
• M = Mass
• r = Radius

❷ To find weight we know that,

${\red{\boxed{\large{\bold{W =\: mg}}}}}$

where,

• W = Weight
• m = Mass
• g = Acceleration due to gravity

Solution :-

❶ First, we have to find the acceleration due to gravity,

Given :

• Mass (M) = 1.9 × 10²⁷ kg
• Gravitational constant (G) = 6.67 × 10-¹¹ Nm²/kg²
• Radius (r) = 71 × 10⁶

According to the question by using the formula we get,

⇒ $\sf g =\: \dfrac{6.67 \times {10}^{-11} \times 1.9 \times {10}^{27}}{(71 \times {10}^{6})^{2}}$

⇒ $\sf g =\: 0.00251 \times {10}^{4}$

⇒ $\sf g =\: 0.00251 \times 10000$

➠ $\sf\bold{\green{g =\: 25.1\: m/{s}^{2}}}$

$\therefore$ The acceleration due to gravity of jupiter is 25.1 m/s² .

❷ Now, we have to find the weight of a person,

Given :

• Mass (m) = 800 kg
• Acceleration due to gravity (g) = 25.1 m/s²

According to the question by using the formula we get,

↦ $\sf W =\: 800 \times 25.1$

➦ $\sf\bold{\green{W =\: 20080\: N}}$

$\therefore$ The weight of a person is 20080 N .