Match the percentage error of the following and choose correct answer.
I : For a cylinder, percentage errors in r and h are 3 and 5 A) 8
then percentage error in V is
II : $T = 2 π \sqrt{\frac{1}{g}}$ , percentage error in T is 2 then B) 11
percentage error in g is
III : For Sphere, percentage error in r is $\frac{1}{3}$ then C) 1
percentage error in volume is D) –1
E) –4

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B, E, C

B, D, C

A, D, C

C, E, B

answer is C.

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Detailed Solution

$\begin{array}{rcl} I : \frac{δ r}{r} \times 100 & = & 3 \frac{δ h}{h} \times 100 = 5 \\ v & = & {πr}^{2} h \Rightarrow \log v = \log π + 2 \log r + \log h \\ \frac{1}{v} δ v \times 100 & = & \frac{2}{r} δ v \times 100 + \frac{δ h}{h} \times 100 \\ = & 6 + 5 = 11 \end{array}$

$\begin{array}{rcl} II : \frac{δ T}{T} \times 100 & = & 2 \\ T & = & 2 π \sqrt{\frac{1}{g}} \Rightarrow \log T = \log 2 π \sqrt{l} - \log \sqrt{g} \\ \frac{1}{T} δ T \times 100 & = & - \frac{1}{2} \frac{1}{g} δ g \times 100 \\ \frac{δ g}{g} \times 100 & = & - 4 \end{array}$

$III : \frac{δ r}{r} \times 100 = \frac{1}{3} c = \frac{4}{3} {πr}^{3} \Rightarrow \log v = \log \frac{4}{3} π + 3 \log r \Rightarrow \frac{1}{v} δ v \times 100 = \frac{3}{r} δ r \times 100 = 1$