Physics 2005 JAMB Past Questions - Question 42: An elastic material has a length of 36cm when a load of 40 N is hung on it and a length of 45 cm when a load of 60 N is hung on it. The original length of the string is

Correct Answer

E

Explanation

 To determine the original length of the elastic material, you can use Hooke's Law, which relates the force applied to an elastic material and its change in length. Hooke's Law is expressed as:

F = k * ΔL

Where:
F is the force applied (in newtons, N),
k is the spring constant (a measure of the material's stiffness),
ΔL is the change in length (in meters, m).

You have two sets of data:

1. When a load of 40 N is hung on it, the length is 36 cm (0.36 m).
2. When a load of 60 N is hung on it, the length is 45 cm (0.45 m).

First, you need to find the spring constant (k) for this material using the first set of data:

40 N = k * (0.36 m)

Now, solve for k:

k = 40 N / 0.36 m
k = 111.11 N/m (approximately)

Now that you have the spring constant, you can use it to find the original length (L0) when no load is applied. You'll use the second set of data:

60 N = 111.11 N/m * ΔL

Solve for ΔL:

ΔL = 60 N / 111.11 N/m
ΔL ≈ 0.540 m

Now, to find the original length, add ΔL to the length when a load of 60 N is applied:

Original Length (L0) = 0.45 m + 0.540 m
L0 ≈ 0.99 meters

The original length of the elastic material is approximately 0.99 meters (or 99 cm).