Download App

Waves and Sound — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsWaves and Sound1 Mark
MCQ
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
  • ✓
    $25 \mathrm{~kg}$
  • B
    $5 \mathrm{~kg}$
  • C
    $12.5 \mathrm{~kg}$
  • D
    $1 / 25 \mathrm{~kg}$
✓

Answer

Correct option: A.
$25 \mathrm{~kg}$
The frequency of vibration of a string $n=\frac{p}{2 l} \sqrt{\frac{T}{m}}$
Also number of loops $=$ Number of antinodes.
Hence, with 5 antinodes and hanging mass of $9 \mathrm{~kg}$.
We have $p=5$ and $T=9 g \Rightarrow n_1=\frac{5}{2 l} \sqrt{\frac{9 g}{m}}$With $3$ antinodes and hanging mass $M$
We have $p=3$ and $T=M g \Rightarrow n_2=\frac{3}{2 l} \sqrt{\frac{M g}{m}}$
$\because \quad n=n \Rightarrow \frac{5}{2 l} \sqrt{\frac{9 g}{m}}=\frac{3}{2 l} \sqrt{\frac{M g}{m}} \Rightarrow M=25 \mathrm{~kg} .$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Waves and Sound→Waves and Sound — all question types→JEE physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The average power dissipation in a pure capacitance in ac circuit is
→
The magnifying power of an astronomical telescope for relaxed vision is $16.$ On adjusting, the distance between the objective and eye lens is $34 \mathrm{~cm}$. Then the focal length of objective and eye lens will be respectively
→
A current of $1.5 A$ flows through a copper voltameter. The thickness of copper deposited on the electrode surface of area $50 cm ^2$ in 20 minutes will be (Density of copper $=9000 kg / m ^3$ and E.C.E. of copper $=0.00033 g / C )$
→
Energy of electron in a orbit of $H-$atom is
→
The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X=0.5 \mathrm{~m}$ to $X=2.5 \mathrm{~m}$ the work done will be approximately equal to
Image
→
When the body has the same temperature as that of surroundings
→
A pendulum clock keeps correct time at $0^{\circ} \mathrm{C}$. Its mean coefficient of linear expansions is $\alpha /{ }^{\circ} \mathrm{C}$, then the loss in seconds per day by the clock if the temperature rises by $t^{\circ} \mathrm{C}$ is
→
The objective of a compound microscope is essentially
→
If the length of second's pendulum is decreased by $2 \%$, how many seconds it will lose per day
→
The coil of a galvanometer consists of $100$ $turns$ and effective area of $1\, square-cm$. The restoring couple is ${10^{ - 8}}\,N - m/radian$. The magnetic field between the pole pieces is $5\, T$. The current sensitivity of this galvanometer will be
→