A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s²)

Solution

Physics sir · 4 steps

The string tilts until its horizontal pull supplies exactly the centripetal force the bob needs.

1. Forces on the bob. Only two forces act on the bob: the tension T along the string and its weight mg downwards. The bob moves in the same circle as the car, so it needs a centripetal force mv²/r pointing towards the centre.
2. Split the tension. The vertical part balances the weight: T cos θ = mg. The horizontal part provides the centripetal force: T sin θ = mv²/r.

   tan θ = v²/rg

3. Put in numbers. tan θ = 20²/(40 × 10) = 400/400 = 1.
4. So. θ = 45° = π/4, which is option (c).

The idea to keep. A bob hanging in a car going round a circle behaves like a conical pendulum: tan θ = v²/rg. The mass and the string length do not matter.

Answer from the NTA final answer key. Solution by PrepWiser.