Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10 m at a speed of 36 km/h. Find the angle (in degree) made by the string of the pendulum with the vertical if this angle does not change during the turn. Take g = 10 m/s 2 .
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Convert the speed from km/h to m/s.
36 \text{ km/h} = \frac{36 \times 1000}{3600} = 10 \text{ m/s}.
Step 2: Calculate the centripetal acceleration (a_c) required for the car to turn.
a_c = \frac{v^2}{r}, where v = 10 m/s and r = 10 m.
Therefore, a_c = \frac{10^2}{10} = 10 \text{ m/s}^2.
Step 3: The forces acting on the pendulum bob are tension (T) and the gravitational force (mg). The angle \theta made with the vertical satisfies:
\frac{T \sin \theta}{T \cos \theta} = \frac{a_c}{g}. Thus, \tan \theta = \frac{a_c}{g}.
Step 4: Calculate \tan \theta using g = 10 m/s^2 and a_c = 10 m/s^2.
\tan \theta = \frac{10}{10} = 1.
Therefore, \theta = \arctan(1) = 45^\circ.
In conclusion, the angle made by the string with the vertical is 45 degrees.
36 \text{ km/h} = \frac{36 \times 1000}{3600} = 10 \text{ m/s}.
Step 2: Calculate the centripetal acceleration (a_c) required for the car to turn.
a_c = \frac{v^2}{r}, where v = 10 m/s and r = 10 m.
Therefore, a_c = \frac{10^2}{10} = 10 \text{ m/s}^2.
Step 3: The forces acting on the pendulum bob are tension (T) and the gravitational force (mg). The angle \theta made with the vertical satisfies:
\frac{T \sin \theta}{T \cos \theta} = \frac{a_c}{g}. Thus, \tan \theta = \frac{a_c}{g}.
Step 4: Calculate \tan \theta using g = 10 m/s^2 and a_c = 10 m/s^2.
\tan \theta = \frac{10}{10} = 1.
Therefore, \theta = \arctan(1) = 45^\circ.
In conclusion, the angle made by the string with the vertical is 45 degrees.
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