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Question

The mass and density of a solid sphere are measured to be (12.4±0.1) kg and (4.60±0.2) kg/m3. The volume of the sphere expressed with error limits is:

A
(15±0.1) m3
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B
(2.7±0.3) m3
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C
(14.6±0.2) m3
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D
(2.69±0.1) m3
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Solution

The correct option is D (2.69±0.1) m3
Given that
m±Δm=(12.4±0.1) kg
So, the fractional error in mass will be.
Δ mm=0.112.4=0.008
Similarly for density ρ±Δρ=(4.60±0.2) kg/m3
So, fraction error in density will be
Δρρ=0.24.60=0.04
Volume of sphere V=mρ=12.44.60=2.69 m3
From this, Fractional error in volume can be written as,
ΔVV=±(Δ mm+Δρρ)
ΔV=±V(Δmm+Δρρ)
ΔV=±2.69(0.008+0.04)=±2.7×0.05
ΔV=±0.1
Volume of sphere with error limits is,
V±ΔV=(2.69±0.1) m3
Hence, option (d) is the correct answer.

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