Answer:
2.97 meters
9.85 m/s^2
Explanation:
Given that :
Period (T1) = 3.45 seconds
When length , l is shortened by 1m, period (T2) = 2.81 seconds
Using the relation :
T = 2π√l/g
g = acceleration due to gravity
T1 = 2π√L/g - - - - (1)
Period 2:
x = shortened length = 1m
T2 = 2π√L-x/g - - - (2)
Square both sides
T1² = (2π)² L/g - - - (3)
T2² = (2π)² L-x/g - - (4)
Divide 3 and 4
(T2/T1)² = (L-x) / L
(2.81/3.45)^2 = (L - 1) / L
0.6633984 = (L - 1) / L
0.6633984L = L - 1
0.6633984L - L = - 1
−0.336601L = - 1
L = 1 / 0.336601
L = 2.9708764
Length = 2.97 meters
Acceleration due to gravity :
g = L(2π/T1)^2
g = 2.97(2π / 3.45)^2
g = 2.97 * 3.3168172
g = 9.8509
g = 9.85 m/s^2
g
