Question

Q20. If percentage errors in the measurement of mass and volume of an object are 2% and 3% respectively, then the percentage error in the measurement of the density of the object is

1 point

A. 1%

B. 0.66%

C. 5%

D. 6%​

Answer 1

Answer:

5%

Explanation:

mass =2%

volume=3%

density = mass/volume

so % error will be

(∆d/d) ×100 =(∆m/m)×100+(∆v/v)×100

d% = m% + v%

d% =2%+3%

d% = 5%

Answer 2

Given:

% errors in the measurement of mass and volume of an object are 2% and 3% respectively.

To find:

The percentage error in the measurement of the density of the object

Solution:

Now, % error in density will be :

$\therefore \: \rho = \dfrac{m}{V}$

Since the individual % error of mass and volume is very small (i.e. < 6%), we can say:

$\implies \dfrac{\Delta \rho}{ \rho} = \dfrac{\Delta m}{m } + \dfrac{\Delta V}{V}$

$\implies \dfrac{\Delta \rho}{ \rho} = 2 \% + 3\%$

$\implies \dfrac{\Delta \rho}{ \rho} = 5\%$

So, % error in density is 5%.