Question

In a Searle's experiment for determination of Young's
Modulus, when a load of 50 kg is added to a 3 meter
long wire micrometer screw having pitch 1 mm needs
to be given a quarter turn in order to restore the
horizontal position of sprit level. Young's modulus of
the wire if its cross sectional area is 10^-5 m² is​

Answer 1

ᴡᴇ ᴋɴᴏᴡ, ʏᴏᴜɴɢ's ᴍᴏᴅᴜʟᴜs ɪs ɢɪᴠᴇɴ ʙʏ :

ᴠ = ʟᴏɴɢɪᴛᴜᴅɪɴᴀʟ sᴛʀᴇss/ ʟᴏɴɢɪᴛᴜᴅɪɴᴀʟ sᴛʀᴀɪɴ

ɪғ ᴛʜᴇ ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴡɪʀᴇ ᴏғ 'ʀ' ᴛʜᴇɴ ᴀ = πʀ²

ᴠ = ᴍɢʟ/ πʀ²ʟ

Answer 2

Answer:

The young modulus of the wire is 6×10¹¹N/m².

Explanation:

From the question we have,

The load=50kg

The length of the wire=3m

The pitch of the screw=1mm=1×10⁻³m

The area of cross-section=10⁻⁵m²

A quarter turn is required to return the spirit level to its horizontal position. So, elongation is calculated as,

$\Delta l=\frac{1}{4} Pitch$

$\Delta l=\frac{1}{4} \times 1\times 10^-^3$   (1)

The young modulus(Y) is calculated as,

$Y=\frac{Fl}{A\Delta l}$     (2)

By inserting the variables in equation (2) we get;

$Y=\frac{50\times 10\times 3}{10^-^5\times \frac{1}{4}\times 1\times 10^-^3 }$

$Y=50\times 10\times 3\times 4\times 10^8$

$Y=6\times 10^1^1\ N/m^2$

Hence, the young modulus of the wire is 6×10¹¹N/m².

#SPJ3