Question

the side of a cube as measured by a vernier calipers of least count 0.1 mm is 60 mm. Find
the uncertainty in the measurement of volume of the cube.
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Answer 1

least count of Vernier calliper= 0.1mm

you should know that least count is considered as absolute uncertainty

so, uncertainty in the measurement of side length of cube , ∆l = 0.1mm

side length of cube , l = 60mm

we know, volume of cube = (side length)³

or, V = l³

differentiating both sides,

or, dV = 3l²dl

or, dV/V = (3l²/l³)dl

or, dV/V = 3(dl/l)

or, ∆V/V = 3 × ∆l/l

here, V = l³ = (60)³ = 216000mm³

so, ∆V/216000 = 3 × (0.1/60)

or, ∆V = 216000 × 0.3/60 = 1080 mm³

hence, uncertainty in the measurement of volume of cube is 1080 mm³

Answer 2

1080 m^3

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