While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of 15° to the horizontal. The speed of the car in kmh-1 is

Question

While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of 15° to the horizontal. The speed of the car in kmh-1 is (A) 60.5 (B) 72.5 (C) 82.5 (D) 92.5

Tardigrade Admin · Accepted Answer

Angle θ is given by tan θ = (v2/rg) or ν2 = 529.2 (with the substitution) ⇒ ν = 23 ms-1 or ν = 23 × (18/5) = 82.5 kmh-1

Q. While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of 15 $^{\circ}$ to the horizontal. The speed of the car in $km h^{- 1}$ is

60.5

72.5

82.5

92.5

106.5

Angle $θ$ is given by
$tan θ = \frac{v ^{2}}{r g}$
or $ν^{2} = 529.2$ (with the substitution)
$\Rightarrow$ $ν = 23 m s^{- 1}$
or $ν = 23 \times \frac{18}{5} = 82.5 km h^{- 1}$

Q. While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of 15∘ to the horizontal. The speed of the car in kmh−1 is