Question

A length of rubber cord is l₁​ meters when a tension of 3 N is applied. The length becomes l₂​ meters when the tension is 4 N. The length of the cord in meters when the tension is increased to 9 N is:

Options:
a. 5(l₂​−l₁​)
b. 6(l₂​−l₁​)
c. 5l₂​−6l₁​
d. 6l₂​−5l₁​

Answer 1

The length of the cord when the tension is increased to 9 N is 4 times the original length, or 4l₁​. Option B is correct.

Step-by-step explanation:

To find the length of the cord when the tension is increased to 9 N, we can use a ratio of the tensions and lengths. Let's call the original length of the cord l₁​ and the final length l₂​. So, we can set up the following equation:

3 N / 4 N = l₁​ / l₂​

Now, we can solve for l₂​:

l₂​ = (4 N * l₁) / 3 N

Simplifying this equation:

l₂​ = (4/3) * l₁​

To find the length of the cord when the tension is increased to 9 N, we can substitute l₂​ with (4/3) * l₁​ in the equation:

l = (9 N * (4/3) * l₁) / 3 N

After simplifying the equation, we get:

l = 4l₁​

So, the length of the cord when the tension is increased to 9 N is 4 times the original length, or 4l₁​.