Question

find a simple pendulum of length 50cm +-0.1cm the time period for 100 oscillations is found to be 50s when observed using a stop watch having resolution of 1s. Find the accuracy in the determination of g​

Answer 1

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11th

Physics

Gravitation

Acceleration due to Gravity

The time period of oscillat...

PHYSICS

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?

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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%