Question

While driving around curve of radius 17.32 m, an engineer notes that a pendulum in his car hangs at an angle of ${30}^{\circ }$ to the vertical The speed of the car is

• A. 10 m/s
• B. 15 m/s
• C. 5 m/s
• D. 6.7 m/s

Answer 1

The correct option is A 10 m/s

Ref. Image.

$Tcos{30}^{\circ }=mg$ _____ (1)

$Tsin{30}^{\circ }=\frac{m{V}^2}{R}$ ______ (2)

Divide both

$tan{30}^{\circ }=\frac{V^2}{Rg}$

$V=\sqrt{Rgtan30}$

$=\sqrt{17.32\times 9.5\times \frac{1}{\sqrt{3}}}$

$=\sqrt{17.32\times 9.5\times \frac{1}{1.732}}$

V = 10 m/s