My problems #11

Classical Mechanics Level 2

. The pitch of a screw gauge is 1 m m 1 \ mm and there are 100 100 divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads 1 1 mm and 4 7 t h 47^{th} division on the circular scale coincides with the reference line. The length of the wire is 5.6 5.6 cm. Find the curved surface area in c m 2 cm^2 of the wire in appropriate number of significant figures assuming there is no zero error in the instrument


The answer is 2.5848.

Siddharth Bhatt by siddharth bhatt , 25, India

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1 solution

Anandhu Raj
Feb 17, 2015

Given Pitch =1 mm and number of divisions=100 ,

Then least count= P i t c h N o . o f d i v i s i o n s o n t h e h e a d s c a l e = 1 m m 100 = 0.01 m m \frac { Pitch }{ No.of\quad divisions\quad on\quad the\quad head\quad scale } =\frac { 1mm }{ 100 } =0.01mm

Diameter of wire= 1+0.47 = 1.47 mm=0.147 cm

Given length = 5.6 cm

CSA of wire = 2 π r h 2\pi rh = 2 π × 0.147 2 × 5.6 = 2.585 c m 2 2\pi \times \frac { 0.147 }{ 2 } \times 5.6=\boxed{2.585\quad { cm }^{ 2 }}

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