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Sagot :
Answer:
- the acceleration of gravity of Jupiter = 25.836 m/s²
- the weight of mass 100 kg on Jupiter = 2583.6 N
Explanation:
To find the gravity of Jupiter, we can compare it with earth's gravity by using this formula:
[tex]\boxed{g=\frac{Gm}{r^2} }[/tex]
where:
- [tex]g=\text{gravitational acceleration}[/tex]
- [tex]G=\text{gravitational constant}[/tex]
- [tex]m=\text{mass}[/tex]
- [tex]r=\text{radius}[/tex]
Given:
- [tex]g_e=9.8\ m/s^2[/tex]
- [tex]m_j=319m_e[/tex]
- [tex]r_j=11r_e[/tex]
Hence:
[tex]\displaystyle g_e:g_j=\frac{Gm_e}{r_e^2} :\frac{Gm_j}{r_j^2}[/tex]
[tex]\displaystyle 9.8:g_j=\frac{m_e}{r_e^2} :\frac{319m_e}{(11r_e)^2}[/tex]
[tex]\displaystyle 9.8:g_j=1 :\frac{319}{121}[/tex]
[tex]\displaystyle g_j=\frac{319}{121}\times9.8[/tex]
[tex]\bf g_j=25.836\ m/s^2[/tex]
To find the weight of an object of mass 100 kg on Jupiter, we can use this formula:
[tex]\boxed{weight(w)=mass(m)\times gravitational\ acceleration(g)}[/tex]
[tex]w_j=m\times g_j[/tex]
[tex]=100\times25.836[/tex]
[tex]=2583.6\ N[/tex]
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