64) The time period of a simple pendulum is 2 s. What is its frequency ? What name is given to such a pendulum ?
f = 1/T = ½ Hz = 0.5 Hz
Time period is 2 sec => That means it’s a seconds’ pendulum
65) A seconds’ pendulum is taken to a place where acceleration due to gravity falls to one-fourth. How is the time period of the pendulum affected, if at all? Give reason. What will be its new time period ?
Time period is inversely proportional to the square root of g
Normal time period = T1 ∞ 1/√g
Time period at new place = T2 ∞ 1/√(g/4) => T2 ∞ 2/(√g)
so, T2/T1 = 2
So at the new place time period will become double of its normal time period.
Here the pendulum is seconds’ pendulum. So normally its time period is 2 secs
So at the new place it would be double i.e. 4 secs.
66) Find the length of a seconds’ pendulum at a place where g = 10 m/s2 (Take ∏= 3·14).
T = 2 ∏ √(L/g)
so, L = T2 g /(4∏2) …(1)
T = 2 seconds
g = 10 m/s2
So, L = (22 x 10)/(4 x 9.86) = 1.014 m