Download App

Question Bank [ 2022 ] — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsQuestion Bank [ 2022 ]3 Marks
Question
Two wires of the same material and same cross-section are stretched on a sonometer. One wire is loaded with $1\ kg$ and another is loaded with $9\ kg.$ The vibrating length of the first wire is $60\ cm$ and its fundamental frequency of vibration is the same as that of the second wire. Calculate the vibrating length of the other wire.
✓

Answer

Given:
$M_1=1 kg , M_2=9 kg$,
$A_1=A_2$
$m _1= m _2$ (where $m$ is linear density of wire)
$L_1=60 cm =0.6 m$
$\left( n _0\right)_1=\left( n _0\right)_2$
To find: Vibrating length of wire $\left(L_2\right)$
Formula:
$n =\frac{1}{2 L } \sqrt{\frac{ T }{ m }}$
Calculation:
From formula,
$( n )_1=\frac{1}{2 L _1} \sqrt{\frac{ T _1}{ m _1}}$
$( n )_2=\frac{1}{2 L _2} \sqrt{\frac{ T _2}{ m _2}}$
$\because(n)_1=(n)_2$
$ \therefore \frac{1}{2 L _1} \sqrt{\frac{ T _1}{ m _1}}=\frac{1}{2 L _2} \sqrt{\frac{ T _2}{ m _2}}$
$\therefore \frac{1}{4 L _1^2} \frac{ T _1}{ m _1}=\frac{1}{4 L _2^2} \frac{ T _2}{ m _2}$
$\therefore L _2=\sqrt{ L _1^2 \times \frac{ T _2}{ m _2} \times \frac{ m _1}{ T _1}}$
$=\sqrt{(0.6)^2 \times \frac{9 g }{1 g }}$
$=0.6 \times 3$
$= 1 . 8\ m $
The vibrating length of the wire is $1.8\ m$.

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 "Answer the following in Brief" from Question Bank [ 2022 ]→Question Bank [ 2022 ] — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

A transformer converts 400 volt ac to 100 volt ac The secondary of the transformer has 50 turns and the load across it draws a current of $600 mA$. What is the current in the primary, the power consumed and the number of turns in the primary?
→
The speed limit for a vehicle on road is \(120 km / hr\). A policeman detects a drop of \(10 \%\) in the pitch of horn of a car as it passes him. Is the policeman justified in punishing the car driver for crossing the speed limit?(Given : Velocity of sound \(=340 m / s\) )
→
Name a non$-\text{SI}$ unit of magnetic induction. State its relation to the $\text{SI}$ unit of magnetic induction.
→

State the conditions for concavity and convexity of a liquid surface where it is in contact with a solid.
→
A particle performs linear S.H.M. of period $4$ seconds and amplitude $4\ cm.$ Find the time taken by it to travel a distance of $1\ cm$ from the positive extreme position.
→
The critical angle for a glass-air interface is $\sin 1 \frac{5}{8}$. A ray of unpolarized monochromatic light in air is incident on the glass. What is the polarizing angle?
→
The energy of $6000 \mathrm{~J}$ is radiated in 5 minutes by a body of surface area $100 \mathrm{~cm}^2$. Find the emissive power (radiant power) of the body.
→
A spherical drop of oil falls at a constant speed of $9.8 cm / s$ in steady air. Calculate the radius of the drop. The density of oil is $0.9013 g / cm ^3$, density of air is $0.0013 g / cm ^3$ and the coefficient of viscosity of air is $1.8 \times 10^{-4}$ poise.
→
In Fraunhoffer diffraction by a narrow slit, a screen is placed at a distance of $2\ m$ from the lens to obtain the diffraction pattern. If the slit width is $0.2\ mm$ and the first minimum is $5\ mm$ on either side of the central maximum, find the wavelength of light.
→
An electric lamp is connected in series with a capacitor and an AC source is glowing with a certain brightness. How does the brightness of the lamp change on increasing the capacitance ?
→