Two inclined frictionless tracks, one gradual and the other steep meet at O, from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time ? Will they reach there with the same speed ? Explain.

Explanation

To solve the problem of whether two stones sliding down frictionless inclined tracks will reach the bottom at the same time and with the same speed, we can follow these steps:

### Step 1: Understand the Setup
We have two inclined tracks meeting at point O. One track is gradual (let's call it Track 1) and the other is steep (Track 2). Both stones start from rest at point O.

### Step 2: Analyze Forces Acting on the Stones
Since both tracks are frictionless, the only force acting on the stones is gravity. The gravitational force can be resolved into two components: one perpendicular to the incline (normal force) and one parallel to the incline (which causes the acceleration down the track).

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