To find the density of a material of the body using moments

[leena19]

1. The problem statement, all variables and given/known data
http://img193.imageshack.us/img193/914/63378846.th.png (http://img193.imageshack.us/my.php?image=63378846.png)
Fig.A shows the balanced position of a light rod carrying an object X and a mass M .
Fig.B shows the balanced position of the same system when X is immersed in water.If the density of water is d,the density of the material made of X is given by,
1) [L1/(L1-L2)]d 2) (L1/L2)d 3) [L1/L1+L2]d 4) [(L1-L2)/L1]d 5) (L2/L1) d

2. Relevant equations



3. The attempt at a solution
Taking moments about the pivot,
for A
mg*l = Mg*L1
m=ML1/l m=mass of X

for B
Mg*L2 = m1g*l
m1= ML2/l m1g = apparent weight of X in water

density of X= (real weight/apparent loss of weight in water) d
=(m/m-m1)*d
=(1-m/m1)d
=(1-L1/L2)*d
gives me( L2-L1/L2)*d, which is not even among the choices given.
I can't figure out where I'm going wrong.

[alphysicist]

Hi leena19,

1. The problem statement, all variables and given/known data
http://img193.imageshack.us/img193/914/63378846.th.png (http://img193.imageshack.us/my.php?image=63378846.png)
Fig.A shows the balanced position of a light rod carrying an object X and a mass M .
Fig.B shows the balanced position of the same system when X is immersed in water.If the density of water is d,the density of the material made of X is given by,
1) [L1/(L1-L2)]d 2) (L1/L2)d 3) [L1/L1+L2]d 4) [(L1-L2)/L1]d 5) (L2/L1) d

2. Relevant equations



3. The attempt at a solution
Taking moments about the pivot,
for A
mg*l = Mg*L1
m=ML1/l m=mass of X

for B
Mg*L2 = m1g*l
m1= ML2/l m1g = apparent weight of X in water

density of X= (real weight/apparent loss of weight in water) d
=(m/m-m1)*d
=(1-m/m1)d

I have not looked over all of your work, but it looks like these last two lines are saying that:


\left(\frac{m}{m-m_1}\right) \to \left(1-\frac{m}{m_1}\right)


which is not true.

[leena19]

Thanks for replying!




I have not looked over all of your work, but it looks like these last two lines are saying that:


\left(\frac{m}{m-m_1}\right) \to \left(1-\frac{m}{m_1}\right)


which is not true.

Oops!
after correcting it ,I get
[L1/(L1-L2)]d which would be answer no.1,hopefully?


EDIT:
The answer is (1).
Thank you very much for the help!