Question:
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form \(y = -0.21\sin(x+30t)\) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is \(x\times10^{-2}\) N. Value of x is _________. (Round off to the nearest integer)
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form \(y = -0.21\sin(x+30t)\) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is \(x\times10^{-2}\) N. Value of x is _________. (Round off to the nearest integer)
Show Hint
Wave speed \(v = \omega/k\) and \(v = \sqrt{T/\mu}\), so \(T = \mu v^2\); convert \(\mu\) to kg/m.
Updated On: Nov 4, 2026
Show Solution
Verified By Collegedunia
Correct Answer: 1215
Solution and Explanation
Comparing with \(y = A\sin(kx+\omega t)\): \(k = 1\) m-1, \(\omega = 30\) rad/s, so \(v = \frac{\omega}{k} = 30\) m/s.
\(\mu = 0.135\) g/cm \(= \frac{0.135\times10^{-3}\text{ kg}}{10^{-2}\text{ m}} = 0.0135\) kg/m.
\(T = \mu v^2 = 0.0135\times 900 = 12.15\) N \(= 1215\times10^{-2}\) N.
Answer: 1215
\(\mu = 0.135\) g/cm \(= \frac{0.135\times10^{-3}\text{ kg}}{10^{-2}\text{ m}} = 0.0135\) kg/m.
\(T = \mu v^2 = 0.0135\times 900 = 12.15\) N \(= 1215\times10^{-2}\) N.
Answer: 1215
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main Waves Questions
- A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ________ m/s.
- The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be :
- Two waves of intensity ratio \( 1 : 9 \) cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is \( I_1 \) (b) Waves are coherent is \( I_2 \) and differ in phase by \( 60^\circ \) If \( \frac{I_1}{I_2} = \frac{10}{x} \) then \( x = \) _____.
- The equation of a stationary wave is:
\[y = 2a \sin\left(\frac{2\pi nt}{\lambda}\right) \cos\left(\frac{2\pi x}{\lambda}\right)\]Which of the following is NOT correct: - A plane progressive wave is given by \( y = 2 \cos 2\pi(330t - x) \, \text{m} \). The frequency of the wave is:
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions