Search any question & find its solution
Question:
Answered & Verified by Expert
A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 \mathrm{~kg}$ is suspended from the wire. When this mass is replaced by a mass $\mathrm{M}$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of ' $M$ ' is
Options:
Solution:
1690 Upvotes
Verified Answer
The correct answer is:
25 kg
For a vibrating wire, we have $\mathrm{Tp}^2=$ constant
Where $\mathrm{p}$ is the number of loops formed and $\mathrm{T}$ is the tension
$$
\begin{aligned}
& \mathrm{T}_1=9 \mathrm{~kg}-\mathrm{wt}, \mathrm{p}_1=5, \mathrm{p}_2=3 \\
& \therefore \mathrm{T}_1 \mathrm{P}_1^2=\mathrm{T}_2 \mathrm{P}_2^2 \\
& \therefore 9 \times 25=\mathrm{T}_2 \times 9 \\
& \therefore \mathrm{T}_2=25 \mathrm{~kg}-\mathrm{wt}
\end{aligned}
$$
Where $\mathrm{p}$ is the number of loops formed and $\mathrm{T}$ is the tension
$$
\begin{aligned}
& \mathrm{T}_1=9 \mathrm{~kg}-\mathrm{wt}, \mathrm{p}_1=5, \mathrm{p}_2=3 \\
& \therefore \mathrm{T}_1 \mathrm{P}_1^2=\mathrm{T}_2 \mathrm{P}_2^2 \\
& \therefore 9 \times 25=\mathrm{T}_2 \times 9 \\
& \therefore \mathrm{T}_2=25 \mathrm{~kg}-\mathrm{wt}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.