A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where x is ______

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 3.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Since least count of the instrument can be calculated as

$Least count = \frac{pitch length}{No. of division on circular scale}$

$= \frac{0.75}{15} = 0.05 mm .$
Here we are provided L = 5 mm & W = 2.5 mm L = 5 mm & W = 2.5 mm
$∵ We know that$
A=L.W
For calculating fractional error, we can write

$\frac{dA}{A} = \frac{dL}{L} + \frac{dW}{W}$

$\begin{aligned} \begin{aligned} \frac{dA}{A} = \frac{0.05}{5} + \frac{0.05}{2.5} \\ \Rightarrow \frac{dA}{A} = \frac{1}{100} + \frac{2}{100} = \frac{3}{100} \end{aligned} \\ So, x = 3 \end{aligned}$