A Second's pendulum is suspended from the roof of a lift.What will be the time period of the Pendulum if the lift is moving up with an acceleration of 2m/sec^2
To determine the time period of the pendulum, we need to understand the factors that affect the time period of a pendulum. The time period of a pendulum is given by the formula:
T = 2π√(L/g),
where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this scenario, the lift is moving up with an acceleration of 2 m/sec^2, which means that the effective value of acceleration due to gravity will be increased or decreased depending on the direction of the acceleration.
If the lift is moving up, the net acceleration acting on the pendulum will be the sum of the acceleration due to gravity and the acceleration of the lift:
Net acceleration = g + a,
where g is the acceleration due to gravity and a is the acceleration of the lift.
Since the pendulum is suspended from the roof of the lift, the effective gravitational acceleration acting on the pendulum will be:
Effective acceleration due to gravity = g - a,
where g is the acceleration due to gravity and a is the acceleration of the lift.
Now, substitute the effective acceleration due to gravity in the formula for the time period of the pendulum:
T = 2π√(L / (g - a)).
Given that the acceleration due to gravity (g) is approximately 9.8 m/sec^2 and the acceleration of the lift (a) is 2 m/sec^2, we can calculate the time period of the pendulum using this formula.