Question

periodic time of simple pendulum is given by T= 2π √ l\ g length of pendulum is measured 100 cm with accuracy of 1 mm periodic time is measured by stopwatch having least count of 0.1 periodic time is 2 sec and time of 100 oscillation is measured calculate percentage error is measured of g

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Answer 1

The time period of oscillation of a simple pendulum is T=2π

(l/g)

.measured value of length is 20cm known to have 1mm accuracy and time for 100 oscillation of the pendulum is found to be 90s using wrist watch of 1s resolution.what is the accuracy in determining the value of acceleration due to gravity?

MEDIUM

ANSWER

T= Time period of one oscillation

t= Time period of 100 oscillation

For 100 oscillation, t=100T

Take ln and differentiate.

t

Δt

=

T

ΔT

=

90

2

.....(1)

Time period of one oscillation

T=2π

g

L

g=4π

2

T

2

L

Take ln on both side and differentiate

g

Δg

=±(

L

ΔL

+2

T

ΔT

)

g

Δg

=±(

20

0.1

+

90

2

)==±2.7%

Hence, error in gravity is ±2.7%