A heavy ball of mass $M$ is suspended from the ceiling of car by a light string of mass $m (m << M)$. When the car is at rest, the speed of transverse waves in the string is $60\, ms^{-1}$. When the car has acceleration $a$ , the wave-speed increases to $60.5\, ms^{-1}$. The value of $a$ , in terms of gravitational acceleration $g$ is closest to
JEE MAIN 2019, Diffcult
Download our app for free and get started
$60=\sqrt{\frac{M g}{\mu}}$
$60.5=\sqrt{\frac{M\left(g^{2}+a^{2}\right)^{1 / 2}}{\mu}} \Rightarrow \frac{60.5}{60}=\sqrt{\sqrt{\frac{g^{2}+a^{2}}{g^{2}}}}$
$\left(1+\frac{0.5}{60}\right)^{4}=\frac{g^{2}+a^{2}}{g^{2}}=1+\frac{2}{60}$
$\Rightarrow g^{2}+a^{2}=g^{2}+g^{2} \times \frac{2}{60}$
$a=g \sqrt{\frac{2}{60}}=\frac{g}{\sqrt{30}}=\frac{g}{5.47}$
$\simeq \frac{g}{5}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two closed organ pipes of length $100 \,cm$ and $101 \,cm$ $16$ beats in $20\, sec$. When each pipe is sounded in its fundamental mode calculate the velocity of sound .... $ms^{-1}$View Solution
- 2Two waves are propagating along a taut string that coincides with the $x-$axis. The first wave has the wave function $y_1 = A cos [k(x - vt)]$ and the second has the wave function $y = A cos [k(x + vt) + \phi ]$.View Solution
- 3View SolutionA perfectly elastic uniform string is suspended vertically with its upper end fixed to the ceiling and the lower end loaded with the weight. If a transverse wave is imparted to the lower end of the string, the pulse will
- 4View SolutionTwo wires are producing fundamental notes of the same frequency. Change in which of the following factors of one wire will not produce beats between them
- 5A train blowing its whistle moves with constant speed on a straight track towards observer and then crosses him. If the ratio of difference between the actual and apparent frequencies be $3: 2$ in the two cases, then the speed of train is [ $v$ is speed of sound]View Solution
- 6Two points on a travelling wave having frequency $500\, Hz$ and velocity $300\, m/s$ are $60^o$ out of phase, then the minimum distance between the two points is ..... $m$View Solution
- 7Two waves are simultaneously passing through a string and their equations are :View Solution
${y}_{1}={A}_{1} \sin {k}({x}-v {t}), {y}_{2}={A}_{2} \sin {k}\left({x}-{vt}+{x}_{0}\right) .$ Given amplitudes ${A}_{1}=12\, {mm}$ and ${A}_{2}=5\, {mm}$ ${x}_{0}=3.5\, {cm}$ and wave number ${k}=6.28\, {cm}^{-1}$. The amplitude of resulting wave will be $......\,{mm}$
- 8View SolutionIn Melde’s experiment in the transverse mode, the frequency of the tuning fork and the frequency of the waves in the strings are in the ratio
- 9An iron block is dropped into a deep well. Sound of splash is heard after $4.23 \,s$. If the depth of the well is $78.4 \,m$, then find the speed of sound in air is ............ $m / s$ $\left(g=9.8 \,m / s ^2\right)$View Solution
- 10A uniform rope having some mass hanges vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed $(v)$ of the wave pulse varies with height $(h)$ from the lower end as:View Solution