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)/(lbh)`
`:.` The relative error is given by
`(Deltad)/(d) = ((DeltaM)/(M))+((Deltal)/(l))+((Deltab)/(b))+((Deltah)/(h))`
Given 1=8.0 cm and `Deltal` = 0.01 cm ,
b=5.0 cm and `Deltab ` =0.01 cm
h=1 mm and `Deltah =0.01 ` mm and
M 33.333g and `Delta`M = 1mg = 0.001g
Hence `(DeltaM)/(M) = (0.001)/(33.333)`
`(Deltal)/(l)=(0.01)/(8.0),(Deltab)/(b) =(0.01)/(5)` and `(Deltah)/(h) = (0.01)/(l)`
The percentage error is given by
`((DeltaM)/(m)+(Deltal)/(l)+(Deltab)/(b)+(Deltah)/(h))xx100`
`=((0.001)/(33.333)+(0.01)/(8.0)+(0.01)/(5)+(0.01)/(1))xx100`
`= 0.003 +0.125 +0.2+1.0= 1.328. `
`1.328~=1.3`
The percentage error is 1.3 %