A car moving with a speed of 54 km/h…

Single correct+4 / -1Answer matches NTA’s final key

A car moving with a speed of 54 km/h 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)

$\tan^{-1}(0.5)$
$\tan^{-1}(0.75)$
$\tan^{-1}(1.125)$
$\tan^{-1}(0.25)$

Solution

In the car's frame the bob feels gravity $mg$ down and a centrifugal force $\frac{mv^2}{r}$ outward. The string lines up with their resultant:

$\tan\theta = \frac{v^2}{rg}.$

$v = 54$ km/h $= 15$ m/s, so $\tan\theta = \dfrac{225}{20 \times 10} = 1.125$ .

Answer: $\tan^{-1}(1.125)$ .

Answer checked against the official answer key. The solution is our own working.

JEE MAIN 2026 · Laws of Motion

Solution

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