Question

Length of wire was 2 m when load was 80 kg. If the load is 120 kg , length becomes 2.2 m.
Find original length of wire.
(A) 1.5 m
(B) 1.6 m
(C) 1.8 m
(D) 1.9 m
Iz
- 2XA​

Answer 1

Answer:

b

Explanation:

1.6 because when the length is 40kg the length will be 0.2m and after removing total weight i.e.80kg the length will be reduced by 0.4m

Answer 2

Answer:

The original length of the wire is 1.6 m.

Explanation:

• Let, the Young's modulus of the given wire be Y.
• The original length of the given wire be L and the cross section area of wire be A.
• Considering, that when load is applied on the wire, there is no change in the cross sectional area and only increase in length.
• Since, the load on the wire is 80 Kg. The force exerted by this load is 80g (where g is acceleration due to gravity).
• The total stretched length of wire is 2m. The elongation produced in the wire is (2 - L) m.
• The Young's Modulus of wire is

$Y = \frac{80g L}{A (2-L)} \: \: - - - (1)$

• When the load on wire is 120 Kg, the force on wire is 120g.
• The elongation produced in wire is (2.2 - L).
• The Young's Modulus of wire is

$Y = \frac{120g L}{A (2.2-L)} \: \: - - - (2)$

• Since, Young's modulus of a wire is constant. Equating equation (1) and (2), we get;

$\frac{80g L}{A (2-L)} = \frac{120g L}{A (2.2-L)} \\ 80(2.2 - L) = 120(2 - L) \\ 176 - 80L = 240 - 120L \\ 40L = 64 \\ L = 1.6 \: m$

• Hence, original length of the wire is 1.6 m .