Question

a car is moving in a circular horizontal track of radius 10 m with a constant speed of 10m/s.A bob is suspended from the roof of carby a string of 1 m.The angle made by stringwith the vertical is?

Answer 1

Answer:

45°

Explanation:

Draw a free body diagram of the bob.  The bob has two forces acting on it.  Tension force in the direction of the string and weight downwards.

Sum of the forces in the y direction:

∑F = ma

T cos θ − mg = 0

Sum of the forces in the x direction:

∑F = ma

T sin θ = m v² / r

Solve for T in the first equation and substitute into the second:

T cos θ = mg

T = mg / cos θ

(mg / cos θ) sin θ = m v² / r

mg tan θ = m v² / r

g tan θ = v² / r

tan θ = v² / (r g)

θ = atan(v² / (r g))

Given v = 10 m/s and r = 10 m, and assuming g = 10 m/s²:

θ = atan(100 / (10 × 10)

θ = atan(1)

θ = 45°

Notice the length of the string and the mass of the bob do not matter.