A uniform thin rope of length 12 , m and mass | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the mass per unit length.S

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the mass per unit length.Since the frequency $f$ of the wavetrain remains constant,$v = f \lambda$,which implies $v \propto \lambda$.At the lower end (bottom),the tension $T_1$ is due to the block of mass $m = 2 \, kg$:$T_1 = mg = 2g$.At the top of the rope,the tension $T_2$ is due to the block and the entire mass of the rope $M = 6 \, kg$:$T_2 = (M + m)g = (6 + 2)g = 8g$.Using the relation $\frac{\lambda_2}{\lambda_1} = \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$:$\lambda_2 = \lambda_1 \sqrt{\frac{8g}{2g}} = 6 	imes \sqrt{4} = 6 	imes 2 = 12 \, cm$.

Similar Questions

$A$ string of length $L$ is stretched by $\frac{L}{20}$ and the speed of transverse waves along it is $v$. The speed of the wave when it is stretched by $\frac{L}{10}$ will be (assume that Hooke's law is applicable).

$A$ string of mass $0.1 \, kg$ is under a tension $1.6 \, N$. The length of the string is $1 \, m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is (in $s$.)

$A$ uniform rope of mass $0.1 \,kg$ and length $2.45 \,m$ hangs from a rigid support. The time taken by a transverse wave formed in the rope to travel through the full length of the rope is (Assume $g = 9.8 \,m/s^2$). (in $\,s$)

$A$ string of mass $m$ and length $l$ hangs from a ceiling as shown in the figure. $A$ wave in the string moves upward. $v_A$ and $v_B$ are the speeds of the wave at points $A$ and $B$ respectively. Then $v_B$ is

$A$ uniform metal wire has length $L$,mass $M$,and cross-sectional area $A$. It is under tension $T$,and $V$ is the speed of a transverse wave along the wire. The density of the wire is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module