Two wire have cross section diameters `d_(1)` and `d_(2)`, length `L_(1)` & `L_(2)` & densities `rho_(1)` & `rho_(2)` such that
`d_(1) : d_(2) : : 1 : 2 , L_(1) : L_(2):: 2 :1` and `rho_(1) : rho_(2) : : 1 : 2`. What weight must be suspended to the `2nd` wire if the transverse wave produced in it has the same speed as that produced in `1st` wire, which bears a load of `10kg wt`.

Explanation

To solve the problem, we need to find the weight that must be suspended to the second wire so that the speed of the transverse wave produced in it is the same as that produced in the first wire. We will use the relationship between the tension in the wires, their densities, and their cross-sectional areas.

### Step-by-Step Solution:

1. **Identify the Given Ratios:**
- Diameter ratio: \( d_1 : d_2 = 1 : 2 \)
- Length ratio: \( L_1 : L_2 = 2 : 1 \)
- Density ratio: \( \rho_1 : \rho_2 = 1 : 2 \)
...