A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length 5.6 cm. [2004]

Question

A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length 5.6 cm. The main scale reading is 1 mm and 47th circular division coincides with the main scale. Find the curved surface area of wire in ${cm}^{2}$ to appropriate significant figure. (use $π = \frac{22}{7}$ ). [2004]

Smart Achievers · Accepted Answer

(2.6)

$Least count, L.C. = \frac{1 mm}{100} = 0.01 mm$

$Diameter = MSR + CSR \times (L.C.)$

$= 1 mm + 47 \times (0.01) mm = 1.47 mm$

$Curved surface area = 2 π r l = 2 π \frac{D}{2} l = π D l$

$= \frac{22}{7} \times 1.47 \times 56 {mm}^{2} = 2.58724 {cm}^{2}$

$= 2.6 {cm}^{2} (Rounding off to two significant figures)$

Solution

Want Us to Email you About Special Offers & Updates?

Solution

Ans. (2.6) Least count, L.C.=1 mm100=0.01 mm Diameter=MSR+CSR×(L.C.) =1 mm+47×(0.01) mm=1.47 mm Curved surface area=2πrl=2πD2l=πDl =227×1.47×56 mm2=2.58724 cm2 =2.6 cm2 (Rounding off to two significant figures)

Want Us to Email you About Special Offers & Updates?