Question

29. A pendulum with a period of 2.00000 s in one location (g=9.80m/s2) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?

Please include all of your steps to the solution.

Answer 1

Answer:

9.82 m/s²

Explanation:

• The time period of a pendulum, a body fixed to a pivot by means of a string, is given by the time it takes to complete a single cycle from right to left or left to right
• The formula is given as :

        ⇒ T = 2π√(L/g) [← Important]

• L represents the length of the string and g is the value of gravity due to acceleration

Original Time Period [To calculate length of the string]

• T = 2π√(L/g)
• 2 = 2π√(L/9.8)
• L = 9.8/π²
• L = 0.99646 m [← Keep in mind, we'll need it later!]

Calculating value of g' (new acceleration)

• T = 2π√(L/g')
• 1.99796 = 2π√0.99646/g' [← From earlier!]
• g' = 9.82 m/s² (approximately)

Hope it helped~