A rectangular metal slab of mass 33.333 g has its length 8.0 cm, breadth 5.0 cm and thickness 1mm. The mass is measured with accuracy up to 1 mg with a senstitive balance. The length and breadth are measured with a vernier calipers having a least count of 0.01 cm. The thickness is measured with a screwgauge of least count 0.01 mm. Calculate the percentage accuracy in density from above measurements.

Explanation

The percentage error itself gives us the percentage accuracy.
`d= ("mass(M)") /( "length(l)" xx "breadth (b)" xx "height(h)" ) = (M)/( l bh)`
`therefore` The relative error is given by
`(Delta d)/( d ) = ((Delta M)/( M) ) + (Delta l)/( l ) + ((Delta b)/( b) ) + ((Delta h)/( h))`
Given I= 8.0 cm and `Delta l = 0.01` cm,
`b= 5.0 and Delta b = 0.01` cm
`h=1mm and Delta h = 0.01` mm and
`M= 33.333g and Delta M= 1 mg = 0.001 g`
Hence, `(Delta M)/( M) = (0.001)/( 33.333)`
`(Delta l )/( l) = (0.01)/( 8.0) , (Delta b)/( b) = (0.01)/( 5) and (Delta h )/( h) = (0.01)/( l)`
The percentage error is given by
`((Delta M)/( m) + (Delta l)/( l) + (Delta b)/( b) + (Deltah)/( h) ) xx 100`
`= ((0.001)/( 33.333) + (0.01)/( 8.0) + (0.01)/( 5) + (0.001)/(1) ) xx 100`
`= 0.003+ 0.125 + 0.2 + 1.0 = 1.328`.
`1.328 ~= 1.3`
The percentage error is 1.3%