THE TIME OF A PENDULUM VARIES AS THE SQUARE ROOT OF IT LENGHT IF THE LENGTH OF A PENDULUM WHICH BEAT 15S IN 9CM FIND A THE LENGHT THAT 80SECONDS B THE TIME OF A PENDULUM WITH LENGHT 36CM
T = k√L
So, T/√L is constant.
So, you want to find L such that 15/√9 = 80/√L
and T such that 15/√9 = T/√36
Please explain more
I want answer
To find the length of a pendulum given the time it takes to complete one full swing, we can use the following formula:
T = 2π√(L/g)
where T represents the time period of the pendulum's swing, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s²).
a) Finding the length for a pendulum with a 15-second time period:
Given: T = 15 s, L = 9 cm = 0.09 m
By rearranging the formula, we can solve for L:
T = 2π√(L/g)
Squaring both sides of the equation eliminates the square root:
T² = (2π√(L/g))²
T² = 4π²(L/g)
Dividing both sides by 4π² and multiplying by g, we get:
L = (T²g) / (4π²)
Plugging in the values, we have:
L = (15² * 9.8) / (4π²) ≈ 1.875 m
Therefore, the length of the pendulum that beats every 15 seconds is approximately 1.875 meters.
b) Finding the time for a pendulum with a length of 36 cm:
Given: L = 36 cm = 0.36 m
Using the same formula:
T = 2π√(L/g)
Plugging in the values, we have:
T = 2π√(0.36 / 9.8) ≈ 2π√0.0367 ≈ 2 * 3.14 * 0.1913 ≈ 1.204 s
Therefore, the time period of a pendulum with a length of 36 cm is approximately 1.204 seconds.