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Question

# The length of cylinder is measured with a metre rod having least count 0.1 cm. Its diameter is measured with vernier caliper having least count 0.01 cm. Given that length is 5.0 cm and diameter is 4.0 cm. The percentage error in the calculated value of the volume will be

A
1.5 %
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B
2.5 %
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C
3.5 %
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D
4 %
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Solution

## The correct option is B 2.5 %Volume of cylinder, V=π r2l=πd24l .........(1) From the data given in the question, Least count of metre rod Δl=0.1 cm Fractional Error in measuring length, Δll=0.15 ⇒% error in measuring length =Δ ll×100=0.15×100=2.0 % From the data given in the question, Least count of vernier calipers Δd=0.01 cm Fractional Error in measuring diameter by vernier calipers, Δ dd=0.014 ⇒% error in measuring diameter =Δ dd×100=0.014×100=0.25% Now, from (1) we can write that, ΔVV=2Δdd+Δll ⇒Δ VV×100=2Δ dd×100+Δ ll×100 ⇒% error in volume =(2×0.25)+(2.0)=2.5% Thus, option (b) is the correct answer.

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