Question

Please help! the mass of an object is measured on a pan balance with a precision of 0.005 g and the recorded value of 128.01 g. a mass of a second object is measured on a pan balance with a precision of 0.005 kg and a recorded value of 0.13 kg. evaluate the claim that these two objects have different masses.

Answer 1

Yes, these two objects have different masses.

How can we calculate that this statement is right ?

To calculate the precision of mass we are using the formula,

Precision(P) = $\frac{m_1}{m_1+\triangle m}$

Or,$\triangle$m=$\frac{m_1}{P}$-m₁

For the first case we are given,

m₁= The recorded value of mass

= 128.01 g

P= Precision of the mass

=0.005g

So, according to the formula, $\triangle$m will be,

$\triangle$m=  $\frac{128.01}{0.005}$-128.01

Or,$\triangle$m=25,473.99 g

Or,$\triangle$m=25.47 Kg

For the first case $\triangle$m is 25.47 Kg..

For the second case we are given,

m₁= The recorded value of mass

= 0.13 Kg

P= Precision of the mass

=0.005 Kg

So, according to the formula, $\triangle$m will be,

$\triangle$m= $\frac{0.13}{0.005}$-0.13

Or,$\triangle$m= 25.87 kg

For the second case $\triangle$m is 25.87 Kg.

For the two cases  $\triangle$m has different values, 25.47 Kg≠25.87 Kg.

Therefore we can conclude that, these two objects have different masses.

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