In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :-

The time period of a simple pendulum is given by:
T = 2π√(L/g)
where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.
The time taken for 20 oscillations is 30 s, so the time period is:
T = 30 s / 20 = 1.5 s
The length of the pendulum is 55.0 cm = 0.55 m.
The least count of the watch is 1 s, and the mean time is 30 s. The percentage error in time is:
ΔT/T = (1 s / 30 s) × 100% = 3.33%
The least count of the meter scale is 1 mm = 0.001 m, and the length is 0.55 m. The percentage error in length is:
ΔL/L = (0.001 m / 0.55 m) × 100% = 0.18%
The formula for g is:
g = 4π²L/T²
Taking the logarithm of both sides:
log g = log(4π²) + log L - 2log T
Differentiating:
Δg/g = ΔL/L - 2(ΔT/T)
Substituting the percentage errors:
Δg/g = 0.18% - 2(3.33%) = 0.18% - 6.66% = -6.48%
The percentage error in g is approximately 6.8%. The negative sign indicates that the error is in the determination of g. Therefore the closest option is 6.8%