Question

the mass and volume of a body is given by M = (12 +_ 0.02 ) kg and v= ( 5 +_ 0.03 )m3. the density of the body is

Answer 1

Answer:2.39 or 2.41

Explanation:

Answer 2

$\frac{+}{}$Given,

Mass, M = (12$\frac{+}{}$ 0.02) kg

Volume, V= (5$\frac{+}{}$0.03) $m^{3}$

To Find,

The density.

Solution,

p=$\frac{M}{V}$

With the help of the error analysis method, we can take algorithm on both sides:

logρ=logM−logV

Differentiating both sides we get,

$\frac{dP}{P} =\frac{dM}{M} -\frac{dV}{V}$

For maximum permissible error,

$\frac{dP}{P} =\frac{dM}{M} +\frac{dV}{V}$

      =$\frac{0.02}{12} +\frac{0.03}{5}$

      = 0.007

Now,

d$(\frac{M}{V} )$= 0.007 ˣ $\frac{12}{5}$

       =0.016 ≈0.01

Density, P= 2.4$\frac{+}{}$0.01 = 2.39 or 2.41 Kg/$m^{3}$

Hence, the density of the body is 2.39 or 2.41 Kg/$m^{3}$