Question

12. The density of a cube is
measured by measuring its mass and
length of its side.li the malmum
error in the measurement of mass
and length are 5 % and 3%
respectively, the maximum error in
the measurement of density is​

Answer 1

Answer:

0.09

Explanation:

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Answer 2

Answer :

Δρ/ρ = 14%

Explanation :

   $\underline{\underline{\bf Errors \ of \ Measurements :}}$

• It is the difference between the true value and the measured value of a quantity.

   $\underline{\underline{\bf Types :}}$

• It can be classified as :

           (a)  systemic errors :

       The systematic errors are those errors that  tend to be in one direction.

           (b)  random errors :

       The random errors are those errors which occur irregularly.

           (c)  least count errors :

        It is associated with the resolution of the instrument.

_________________________________

we know,

          $\bf Density =\frac{mass}{volume}$

Given, (of a cube)

• the maximum error in the measurement of mass = 5%
• the maximum error in the measurement of length = 3%

To find,

• the maximum error in the measurement of density = ?

Solution,

     volume of cube = (length)³

                 $\bf Density =\frac{mass}{(length)^3} \\\\ \implies \rho =\frac{m}{l^3}$

=> the maximum error in the measurement of mass,

           $\bf \frac{\triangle m}{m} =5\%$

=> the maximum error in the measurement of length,

            $\bf \frac{\triangle l}{l} =3\%$

=> the maximum error in the measurement of density,

             $\bf \frac{\triangle \rho}{\rho} =?$

          $\bf \rho=\frac{m}{l^3} \\\\ \boxed{\frac{\triangle \rho}{\rho} =\frac{\triangle m}{m} +3\frac{\triangle l}{l} } \\\\\\ \frac{\triangle \rho}{\rho}=5\%+3(3\%) \\\\ \frac{\triangle \rho}{\rho}=5\%+9\% \\\\ \frac{\triangle \rho}{\rho}=14\% \\\\ \frac{\triangle \rho}{\rho}=0.14$

Therefore, the maximum error in  the measurement of density is​ 14%