Question

In an experiment with a simple pendulum the error in measurement of length 1 of the pendulum 0.1%and time period T is 2% then calculate the maximum possible percentage error in the value of g?

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Answer 1

Answer:

The period of a simple pendulum is given by T=2π

g

l

or T

2

=

g

4π

2

l

or g=

T

2

4π

2

l

As 4 and π are constant, the maximum permissible error in g is given by

g

Δg

=

l

Δl

+

T

2ΔT

here ΔL=0.1cm,L=1m=100cm, ΔT=0.1s,T=50s.∴

g

Δg

=

100

0.1

+2(

50

0.1

)=

100

0.1

+(

25

0.1

);

g

Δg

×=[

100

0.1

+

25

0.1

]×100=0.1+0.4=0.5%.Now g=

T

2

4π

2

l

2

. Here T=

25

50

=2. Therefore,g

′

=

(2)

2

4×(3.14)

4

×(1)

2

=9.8596ms

−2

;Actual value g=9.7720ms

−1

. ThereforePercentage error=

g

g

′

−g

×100=

9.7720

9.8596−9.7720

×100=0.8964%