Two strings of the same material and the same area of cross-section are used in an wxperiment. One is loaded with 12 kg and the other with 3 kg The fu

Question

Two strings of the same material and the same area of cross-section are used in an wxperiment. One is loaded with 12 kg and the other with 3 kg The fu

Two strings of the same material and the same area
of cross-section are used in an wxperiment. One is
loaded with 12 kg and the other with 3 kg The
fundamental fequency of the first string is equal to
the first overtone of the second string. If the length of
the second string is 100 cm, then the length of the
first string is
A. 300 cm
B. 200 cm
C. 100 cm
D. 50 cm

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - c
The frequency of the string
`n = 1/(2l) sqrt(T/m)=1/(2l) sqrt((Mg)/(pir^(2)d))(because T=Mg, m = pi r^(2)d)`
`rArr n_(1) =1/(2l_(1)) sqrt((Mg)/(pir^(2)d))and n_(2) =2/(2l_(2)) sqrt((M_(2)g)/(pir^(2)d))`
From the question`n_(1) n_(2) rArr l_(2)/l_(1)=2sqrt(M_(2)/M_(1)`
`rArr 100/l_(1) = 2sqrt(3/12)=2sqrt(1/4)=2xx1/2rArrl_(1)=100` cm