Question

Mass and volume of a block are measured as 22.42g and 4.7cm^3tge maximum possible error

Answer 1

Answer:

Error in Density  = 0.10153 g/cm3

Explanation:

Full question statement is ;

A certain body weight  22.42gm and has a measured volume of 4.7 c.c. the possible error in the measurement of mass and volume are 0.01gm and 0.1cc.then maximum error in the density will be?

Solution

Mass of body = 22.42 g

Volume of body = 4.7 cc

Density = mass/volume=22.4/24.7

= 4.77021 g/cm3

Error in measurement of mass = 0.01 g

So Mass = 22.42 - 0.01 = 22.41 g

Error in measurement of Volume = 0.1 cc

So Volume = 4.7 - 0.1 = 4.6 cc

Now Density = mass/volume=22.414.6

= 4.87174 g/cm3

Error in Density = 4.87174 - 4.77021 = 0.10153 g/cm3

Answer 2

your complete question is -> A certain body weight 22.42gm and has a measured volume of 4.7 c.c. the possible error in the measurement of mass and volume are 0.01gm and 0.1cc.then maximum error in the density will be....

solution : density = mass/volume

let d is density , m is mass and v is volume of given body .

here, m = 22.42g , v = 4.7 cc = 4.7 cm³

so, density, d = m/v = 22.42/4.7

= 4.77021277 ≈ 4.77 g/cm³

now using formula,

∆d/d = ∆m/m + ∆v/v

⇒∆d/4.77 = 0.01/22.42 + 0.1/4.7

⇒∆d = 4.77(0.01/22.42 + 0.1/4.7)

⇒∆d = 0.10361692637 ≈ 0.1036 g/cm³

hence, maximum error on density is 0.1036 g/cm³ .

percentage error in density = ∆d/d × 100

= 0.1036/4.77 × 100

= 10.36/4.77 ≈ 2.1 %