A car moving with a speed of 54 km/hr takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car

Question

A car moving with a speed of 54 km/hr takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g = 10 m / s^{2}$ ) [2026]

Smart Achievers · Accepted Answer

(3)

$Tension should be opposite to the resultant of \frac{m v^{2}}{r} and m g so that$

$the net force is zero with respect to the observer$

$\tan θ = \frac{\frac{m v^{2}}{r}}{m g} = \frac{v^{2}}{r g}$

$v = 54 km/hr = 15 m/s$

$\tan θ = \frac{v^{2}}{r g}$

$\Rightarrow θ = \tan^{- 1} (1.125)$

Solution

Q.
A car moving with a speed of 54 km/hr takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g = 10 m / s^{2}$ ) [2026]

1 $\tan^{- 1} (0.5)$

2 $\tan^{- 1} (0.75)$

3 $\tan^{- 1} (1.125)$

4 $\tan^{- 1} (0.25)$

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Solution

Q. A car moving with a speed of 54 km/hr takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take g=10 m/s2) [2026]

1 tan-1(0.5)

2 tan-1(0.75)

3 tan-1(1.125)

4 tan-1(0.25)