Question

If the length of a `17 cm` spring increases to `61 cm` when a `4 kg` weight is hanging from it, what is the spring's constant?

Answer 1

See Below.

Explanation:

We know,

The linear expansion of a elastic body is directly proportional to the force exerted on it.

So, `F prop -Deltax`. [The minus is to show that the body is trying to regain its original shape.]

So, `F= -kDeltax` [`k` is the constant of proportionality and `k != 0`]

Now, Subsititute The Values in the relation.

`color(white)(xx)F = -kDeltax`

`rArr mg = -k(61 - 17)` [Here, `F = mg`]

`rArr 4 xx 10 = -kxx44` [Taking `g = 10` `m/s^2`]

`rArr k = -(cancel4 xx 10)/cancel44_11`

`rArr k = -10/11`

Hence Explained.