A broad pipe having a radius `10 cm` branches into two pipes of radii `5 cm` and `3cm`. If the velocity of flowing water in the pipe of radius `3 cm` is `5 cm//s`, determine the velocities of water in the remaining two pipes. Given that the rate of discharge through the main branch is `600picm^(3)//s`.

Explanation

To solve the problem, we will use the principle of conservation of mass, which states that the mass flow rate must remain constant in a closed system. This is often expressed using the continuity equation for fluids, which relates the cross-sectional area and velocity of fluid flow in different sections of a pipe.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Radius of the main pipe, \( R = 10 \, \text{cm} \)
- Radius of pipe 1, \( R_1 = 5 \, \text{cm} \)
- Radius of pipe 2, \( R_2 = 3 \, \text{cm} \)
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