Question

THE MASS OF THE CUBE IS 2g WITH A ERROR OF 0.2g AND THE VOLUME OF CUBE IS 1 cm CUBE WITH ERROR OF 0.1 cm CUBE. FIND THE PERCENTAGE ERROR IN DENSITY.. IF ANYONE SOLVE THIS I WILL FOLLOW AND MARK HIM BRAINLIST ANSWER..​

Answer 1

Answer:

THE MASS OF THE CUBE IS 2g WITH A ERROR OF 0.2g AND THE VOLUME OF CUBE IS 1 cm CUBE WITH ERROR OF 0.1 cm CUBE. FIND THE PERCENTAGE ERROR IN DENSITY.. IF ANYONE SOLVE THIS I WILL FOLLOW AND MARK HIM BRAINLIST ANSWER..

Answer 2

Given:

Mass of the cube = 2g

Error in the mass = 0.2g

Volume of cube = 1cm³

Error in the volume = 0.1cm³

To find:

Percentage error in Density.

Solution:

It is given, mass of the cube, m = 2g

                 error or uncertainty in the mass, Δm = 0.2g

                  volume of the cube, V = 1cm³

                 error or uncertainty in the volume, ΔV = 0.1cm³

Formula used to calculate density is,

       $d = \frac{m}{V}$

here, d = density

        m = mass

         V = volume

by putting all the values we get,

        $d = \frac{2}{1}$

        d = 2 gcm⁻³

now, for errors

      $\frac{\Delta d }{d} = \frac{\Delta m}{m} + \frac{\Delta V}{V}$

by substituting all the values we get,

       $\frac{\Delta d}{d} = \frac{0.2}{2} + \frac{0.1}{1}$

      $\frac{\Delta d }{d} = 0.1 + 0.1$

      Δd = 0.2 × 2

     Δd = 0.4

Now, relative error is $\frac{\Delta d}{d}$

            $\frac{\Delta d}{d} = \frac{0.4}{2}$

                  = 0.2

Now, percentage error will be calculated as follows,

  percentage error = relative error × 100

                                  = 0.2 × 100

    percentage error = 20%

Therefore, Percentage error in density of a cube is 20%.