Q 11-04-051JEE MainJEE Main 2026 (8 Apr, Shift 2)Medium
A car moving with a speed of $54\ \text{km/h}$ 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 $g = 10\ \text{m/s}^2$)
Answer: (C) $\tan^{-1}(1.125)$
$v = 54$ km/h $= 15$ m/s. In the car's frame the bob feels gravity $mg$ downward and a centrifugal force $\dfrac{mv^2}{r}$ outward.
The string lines up with the resultant, so
$$\tan\theta = \frac{v^2}{rg} = \frac{15^2}{20 \times 10} = \frac{225}{200} = 1.125$$
$\theta = \tan^{-1}(1.125)$.
Solution by Sreeraj P, M.Sc Physics