How Does Jupiter's Mass Density Compare to Earth's?

[abuhotlove]

1. The planet Jupiter has an average radius 10.95 times that of the average radius of the Earth and a mass 317.4 times that of the Earth. Calculate the ratio of Jupiter’s mass density to the mass density of the Earth.

2. Show that the expression x = vt + ½ at is dimensionally correct , where x is a
coordinate and has units of length, v is speed, a is acceleration, and t is time.

 

[Redbelly98]

Welcome to PF

First show us what you know, and your thoughts about how to solve the problems. (That's how things work here.)

 

[abuhotlove]

for the (2) I did something like this x=L, V=LT^-1, t=T, a=LT^-2 and t^2 = T^2
there4 the eqn is L= LT^-1*T +1/2 LT^-2*T^2
L= L+1/2 L
So I don't know if it is correct so I need help and the first 1 I'm thinking of solving 4 mass/volume bt i don't knw if it correct and that of the Earth I don't know
Pls can u help me on this.
thnx

 

[Redbelly98]

for the (2) I did something like this x=L, V=LT^-1, t=T, a=LT^-2 and t^2 = T^2
there4 the eqn is L= LT^-1*T +1/2 LT^-2*T^2
L= L+1/2 L
So I don't know if it is correct so I need help

That's good. Then you'd want to remark that each term in the equation has the same dimensions (L). The "1/2" doesn't matter.

If instead you had something like

L = T + 1/2 L T^-1​

that would be a problem, because one can't say a length is equal to a time, also one can't add a time to a velocity (L T^-1)

... and the first 1 I'm thinking of solving 4 mass/volume bt i don't knw if it correct and that of the Earth I don't know
Pls can u help me on this.
thnx

Yes, we'll use

density = mass/volume​

And you can start by writing an expression for the Earth's density. Let it have mass "Me" and radius "Re", how would you express the density of Earth?

 

[abuhotlove]

that I don't know may be u can help me. but I know of desity of the Earth = M/(4pair^3/3)
thnx just help on that I find it difficult that is why I need ur help.
thnx

 

[abuhotlove]

the for the eqn of motion the answer in the text said I should solve so that L=L but I got L =3L bcos L+1/2L = 3L , so can u help me too so that I can arrive @ d answer .
thnx

 

[Redbelly98]

that I don't know may be u can help me. but I know of desity of the Earth = M/(4pair^3/3)
thnx just help on that I find it difficult that is why I need ur help.
thnx

Okay, yes, that's the density of Earth. But I'm just going to rewrite it:

density of Earth = M/(4 pi r^3/3)​

Next step is to write out the density of Jupiter.
Last step will be to take the ratio of the two densities and work through some algebra.

 

[Redbelly98]

the for the eqn of motion the answer in the text said I should solve so that L=L but I got L =3L bcos L+1/2L = 3L , so can u help me too so that I can arrive @ d answer .
thnx

I would look at an example problem from your book or teacher's lecture. That will (hopefully) show how you did indeed get L=L, the correct answer.

 

[abuhotlove]

thnx but 1 thing am confuse about is that d mass and radius of the Earth is not given but that of Jupiter is given so how can I calculate 4 earth?

 

[abuhotlove]

ok the questn is an exercise in a text, which I supplied d question to u. then at d back of the text the answer is L=L ie x=L = right hand side = L too, so it bcomes L=L so I don't know how they got that.

 

[Redbelly98]

thnx but 1 thing am confuse about is that d mass and radius of the Earth is not given ...

That's okay. Just leave the expression as it is,

density of Earth = M/(4 pi r^3/3)​

where M is the mass of the Earth and r is the radius of the Earth.

... but that of Jupiter is given so how can I calculate 4 earth?

Since they don't actually ask for the density of the Earth, it is not necessary to calculate it.

Can you write an expression for the density of Jupiter now?

 

[Redbelly98]

ok the questn is an exercise in a text, which I supplied d question to u. then at d back of the text the answer is L=L ie x=L = right hand side = L too, so it bcomes L=L so I don't know how they got that.

What I meant was, you'll need a completely solved example to look at.

Also, in the future please ask different questions in different separate posts. It gets confusing talking about different problems together.

 

[abuhotlove]

it still the same formula

 

[Redbelly98]

it still the same formula

Well, not quite. M is the density of the Earth, and r is the radius of the Earth. You would need to use the mass and radius of Jupiter instead.

Hint: the mass of Jupiter is 317.4M, according to the problem statement.

 

[Redbelly98]

p.s. I'll be logging off the internet for a while. Good luck!