A wire of $10^{-2} kgm^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^o$ with the horizontal. Masses $m$ and $M$ are tied at two ends of wire such that m rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 ms^{^{-1}}$.

  • A

    $M = 5\,\, kg$

  • B

    $\frac{m}{M}$ $=\frac{1}{4}$

  • C

    $m = 20 \,\,kg$

  • D

    $\frac{m}{M}=4$

Similar Questions

One end of a long string of linear mass density $8.0 \times 10^{-3}\;kg m ^{-1}$ is connected to an electrically driven tuning fork of frequency $256\; Hz$. The other end passes over a pulley and is tied to a pan containing a mass of $90 \;kg$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t=0,$ the left end (fork end) of the string $x=0$ has zero transverse displacement $(y=0)$ and is moving along positive $y$ -direction. The amplitude of the wave is $5.0\; cm .$ Write down the transverse displacement $y$ as function of $x$ and $t$ that describes the wave on the string.

A rope of length $L$ and uniform linear density is hanging from the ceiling. A transverse wave pulse, generated close to the free end of the rope, travels upwards through the rope. Select the correct option.

  • [KVPY 2019]

The speed of a transverse wave passing through a string of length $50 \;cm$ and mass $10\,g$ is $60\,ms ^{-1}$. The area of cross-section of the wire is $2.0\,mm ^{2}$ and its Young's modulus is $1.2 \times 10^{11}\,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5}\; m$. The value of $x$ is $...$

  • [JEE MAIN 2022]

A transverse wave travels on a taut steel wire with a velocity of ${v}$ when tension in it is $2.06 \times 10^{4} \;\mathrm{N} .$ When the tension is changed to $T$. the velocity changed to $\frac v2$. The value of $\mathrm{T}$ is close to

  • [JEE MAIN 2020]

A wire of variable mass per unit length $\mu = \mu _0x$ , is hanging from the ceiling as shown in figure. The length of wire is $l_0$ . A small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach to the other ends