A simple pendulum suspended from the ceiling of a train has a period 'T' when the train is at rest. When the train is accelerating with a uniform acceleration, the time period of simple pendulum will:

Explanation

Understanding the concept:The time period of a simple pendulum is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. When the train accelerates, an additional pseudo force acts on the pendulum bob in the opposite direction of the train's acceleration. This pseudo force effectively increases the "effective gravity" experienced by the pendulum. 2. Calculating effective gravity:When the train accelerates horizontally with acceleration 'a', the pendulum bob experiences two accelerations: 'g' vertically downwards and 'a' horizontally. The effective acceleration (g_eff) is the vector sum of these two accelerations.g_eff = √(g² + a²) 3. Calculating the new time period:The new time period (T') will be:T' = 2π√(L/g_eff) = 2π√(L/√(g² + a²))4. Comparing T' and T:Since g_eff > g, the denominator in the equation for T' is larger than the denominator in the equation for T. Therefore, T' < T.Conclusion:When the train accelerates, the time period of the simple pendulum decreases.