Question

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s-1. A bob is suspended from the roof of the car by a light wire of length 1.0 m. The angle made by the wire with the vertical is (in radian)

• A. 0
• B. π/6
• C. π/3
• D. π/4

Answer 1

Answer: (D)

π/4

Answer 2

At any point on the circular track, the bob is subject to two forces: The tension force in the wire, acting towards the center of the circle. The gravitational force, acting vertically downward.
Since the car is moving with a constant speed, the bob is in equilibrium, and the net force acting on it must be zero. Considering the forces in the vertical direction, we have:
Tension force (T) * cos(θ) - Weight (mg) = 0
Considering the forces in the horizontal direction, we have:
Tension force (T) * sin(θ) = Centripetal force (mv²/r)
We can now solve these equations to find the angle θ.
From the equation T * cos(θ) - mg = 0, we have T = mg / cos(θ).
Substituting this value of T into the equation T * sin(θ) = mv²/r, we get:
(mg / cos(θ)) * sin(θ) = mv²/r
Simplifying, we have: tan(θ) = v² / (rg)
Given that v = 10 m/s and r = 10 m, we can calculate the value of tan(θ):
tan(θ) = (10²) / (10 * 10) = 1
To find the angle θ, we take the inverse tangent (arctan) of both sides:
θ = arctan(1)
θ = π/4
Therefore, the angle made by the wire with the vertical is π/4 radians (option D).