Question

A simple pendulum makes 120 complete oscillations in 3.00 min at a location where g 5 9.80 m/s2. Find (a) the period of the pendulum and (b) its length.

Answer 1

The period of the pendulum is 1.49 seconds and its length is 5.01 meters.

Step-by-step explanation:

(a) To find the period of the pendulum, we can use the formula:

T = 2π√(L/g)

Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. We are given the number of oscillations in a given time period, so we can calculate the number of oscillations per second: 120 oscillations / 180 seconds = 0.67 oscillations/second. The period is the inverse of the frequency, so the period is 1/0.67 = 1.49 seconds (rounded to two decimal places).

(b) To find the length of the pendulum, we can rearrange the formula:

L = gT² / (4π²)

Plugging in the known values, L = (9.80 m/s²)(1.49 s)² / (4π²) = 5.01 meters (rounded to two decimal places).

Answer 2

(a) 1.5 second

(b) 0.56 m

Step-by-step explanation:

Pendulum makes 120 oscillations in 3 min that means in 180 seconds

time taken by the pendulum to complete one oscillation is called time period.

(a) So, the time period is 180 / 120 = 1.5 second

T = 1.5 second

Thus, the time period of the pendulum is 1.5 second.

(b) g = 9.8 m/s^2

The formula for the time period is given by

`T =2\pi \sqrt{(L)/(g)}`

Where, L be the length of pendulum

`1.5 =2* 3.14 \sqrt{(L)/(9.8)}`

`0.057= {(L)/(9.8)}`

L = 0.56 m

Thus, the length of the pendulum is 0.56 m .