Question
In a resonance column first and second resonance are obtained at depths 24 ~cm and 78 ~cm the third resonance will be obtained at depth.
BITSAT
Physics
Oscillations
2022
BITSAT 2022
BITSAT Physics Question (2022) — Solution
Options
- A. 160 ~cm
- B. 132 ~cm
- C. 131 ~cm
- D. 152 ~cm
Answer
B. 132 ~cm
Step-by-step solution
Given, first resonance column at depth, l_1=24 ~cm Second resonance column at depth, l_2=78 ~cm Third resonance column at depths, l_3= ? As aligned & l_1+x= 4 =24 (i)\\ & l_2+x= 3 4 =78 (ii)\\ & l_3+x= 5 4 (iii) aligned From Eqs. (i) and (ii), x= l_2-3 l_1 2 = 78-3(24) 2 =3 (iv) From Eqs. (iii) and (i), l_3+x l_1+x =5 l_3=5 l_1+5 x-x=5 l_1+4 x Substituting l_1 and x value, we get l_3=5(24)+4(3) l_3=132 ~cm .
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