Question

A simple pendulum attached to the ceiling of a car has a time period of 2 sec. If the car accelerates at 2m/s^2 along the x axis, the time period of pendulum

• A. Will increase
• B. Will decrease
• C. Will remain same
• D. Will depend on the tension in the string

Answer 1

The correct option is B Will decrease

The net acceleration if the car is moving in the forward direction is $a^{\prime }=\sqrt{g^2+a^2}=\sqrt{100+4}=10.2m/s^2$
The time period of oscillations will be $T^{\prime }=2\pi \sqrt{L/g^{\prime }}$
$\left(T^{\prime }/T\right)=\sqrt{g/g^{\prime }}=\sqrt{10/10.2}=0.991T$
The correct option is (b)