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Shear Strain

What is the f...

Question

What is the function of a screw gauge in the experiment of determining Young's modulus of a wire?

A

It measures the extension in the wire.

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B

It measures the diameter of the wire.

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C

It measures the load applied.

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D

It measures the length of the wire.

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Solution

The correct option is B It measures the diameter of the wire.
Screw gauge is used to measure the diameter $(d)$ of the wire so that the area of cross-section is calculated by the formula
$A = \frac{π d^{2}}{4}$

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Q. A student performs an experiment to determine the Young's modulus of a wire exactly

2 m

long by Searle's method. In a particular reading, he measures the extension in the length of the wire to be

0.8 m m

with an uncertainty of

\pm 0.05 m m

at a load of exactly

1.0 k g

. He also measures the diameter of the wire to be

0.4 m m

with an uncertainty of

\pm 0.01 m m

. The Young's modulus obtained from the reading is:

(Given Young's Modulus of a wire is given by

Y = \frac{F l}{A e}

F

is the force applied on the wire,

l

is the length of the wire,

A

is the area of cross section of the wire and

e

is the elongation produced in the wire due to the load. Take

g = 9.8 m / s^{2}

Q. A student performs an experiment to determine the Young's modulus of a wire, exactly

2 m

along. by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be

0.8 m m

with an uncertainty of

0.05 m m

at a load of exactly

1.0 k g

. The student also measures the diameter of the wire to be

0.4 m m

with an uncertainty of

0.01 m m

g = 9.8 m s^{- 2}

(exact). The Young's modulus obtained from the reading is

Q. A student performs an experiment to determine the Young's modulus of a wire, exactly

2 m

long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be

0.8 m m

with an uncertainty of

\pm 0.05 m m

at a load of exactly

1.0 k g

. The student also measures the diameter of the wire to be

0.4 m m

with an uncertainty of

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g = 9.8 m / s^{2}

(exact). The Young's modulus obtained from the reading is :

In a Searle's experiment, the diameter of the wire as measured by a screw gauge with least count 0.001 cm is 0.050 cm. The length, measured by a scale of least count 0.1 cm, is 110.0 cm. When a weight of 50 N is suspended from the wire, the extension is measured to be 0.125 cm by a micrometer of least count 0.001 cm. Find the maximum error in the measurement of Young's modulus of the material of the wire from these data.

$y = \frac{W}{A} \times \frac{L}{X}$

Q. A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the students measures the extension in the length of the wire to be 0.8 mm with an uncertainty of +/- 0.05 mm at a load of exactly 1kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of +/-0.01 mm.The Young’s modulus obtained from the reading is

(g = 9.8 m s^{- 2})

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