34. Let F

o

be the buoyant force of air exerted on the object (of mass m and volume V ), and F

brass

be the

buoyant force on the brass weights (of total mass m

brass

and volume V

brass

). Then we have

F

o

= ρ

air

V g = ρ

air

mg

ρ



and

F

brass

= ρ

air

V

brass

g = ρ

air

m

brass

ρ

brass



.

For the two arms of the balance to be in mechanical equilibrium, we require mg

− F

o

= m

brass

g

− F

brass

,

or

mg

− mg

ρ

air

ρ



= m

brass

g

− m

brass

g

ρ

air

ρ

brass



,

which leads to

m

brass

=

1

− ρ

air

/ρ

1

− ρ

air

/ρ

brass



m .

Therefore, the percent error in the measurement of m is

∆m

m

=

m

− m

brass

m

= 1

−

1

− ρ

air

/ρ

1

− ρ

air

/ρ

brass

=

ρ

air

(1/ρ

− 1/ρ

brass

)

1

− ρ

air

/ρ

brass

=

0.0012(1/ρ

− 1/8.0)

1

− 0.0012/8.0

≈ 0.0012

1

ρ

−

1

8.0



,

where ρ is in g/cm

3

. Stating this as a percent error, our result is 0.12% multiplied by



1
ρ

−

1

8.0



.