# Answer the following. A wire gets stretched by 4 mm due to a certain load. If the same load is applied to a wire of same material with half the length and double the - Physics

Sum

A wire gets stretched by 4 mm due to a certain load. If the same load is applied to a wire of same material with half the length and double the diameter of the first wire, what will be the change in its length?

#### Solution

Given: l1 = 4 mm = 4 × 10-3 m

L2 = "L"_1/2, D2 = 2D, r2 = 2r1

To find: Change in length (l2)

Formula: Y = "FL"/("A"l) = "FL"/(pi"r"^2l)

Calculation:

From formula,

"Y"_1 = ("F"_1"L"_1)/(pi"r"_1^2l_1)      .....(i)

"Y"_2 = ("F"_2"L"_2)/(pi"r"_2^2l_2)      .....(ii)

Dividing equation (ii) by equation (i),

"Y"_2/"Y"_1 = (("F"_2"L"_2)/(pi"r"_2^2l_2))/(("F"_1"L"_1)/(pi"r"_1^2l_1))     .....(iii)

Since same load is applied on same wire, Y1 = Y2 and F1 = F

∴ "L"_1/("r"_1^2 l_1) = "L"_2/("r"_2^2l_2)    .....[From (iii)]

l_2 = ("L"_2 xx "r"_1^2 xx l_1)/("r"_2^2 xx "L"_1)

= ("L"_2 xx "r"_1^2 xx l_1)/(4"r"_1^2 xx 2 xx "L"_2)     .....(because "L"_1 = 2"L"_2, "r"_2 = 2"r"_1)

= l_1/8

= (4 xx 10^-3)/8

= 0.5 × 10-3 m

= 0.5 mm

The new change in length of the wire is 0.5 mm.

Concept: Elastic Modulus
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Chapter 6: Mechanical Properties of Solids - Exercises [Page 113]

#### APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 6 Mechanical Properties of Solids
Exercises | Q 5. (iv) | Page 113
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