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
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]
- A
$\frac{g}{{30}}$
- B
$\frac{g}{{10}}$
- C
$\frac{g}{{5}}$
- D
$\frac{g}{{20}}$
Similar Questions
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg m ^{-1} .$ What is
$(a) $ the speed of a transverse wave on the string, and
$(b)$ the tension in the string?
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg m ^{-1} .$ What is
$(a) $ the speed of a transverse wave on the string, and
$(b)$ the tension in the string?
A $20 \mathrm{~cm}$ long string, having a mass of $1.0 \mathrm{~g}$, is fixed at both the ends. The tension in the string is $0.5 \mathrm{~N}$. The string is set into vibrations using an external vibrator of frequency $100 \mathrm{~Hz}$. Find the separation (in $cm$) between the successive nodes on the string.
A $20 \mathrm{~cm}$ long string, having a mass of $1.0 \mathrm{~g}$, is fixed at both the ends. The tension in the string is $0.5 \mathrm{~N}$. The string is set into vibrations using an external vibrator of frequency $100 \mathrm{~Hz}$. Find the separation (in $cm$) between the successive nodes on the string.
- [IIT 2009]
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :
- [NEET 2022]
A composition string is made up by joining two strings of different masses per unit length $\rightarrow \mu$ and $4\mu$ . The composite string is under the same tension. A transverse wave pulse $: Y = (6 mm) \,\,sin\,\,(5t + 40x),$ where $‘t’$ is in seconds and $‘x’$ in meters, is sent along the lighter string towards the joint. The joint is at $x = 0$. The equation of the wave pulse reflected from the joint is
A composition string is made up by joining two strings of different masses per unit length $\rightarrow \mu$ and $4\mu$ . The composite string is under the same tension. A transverse wave pulse $: Y = (6 mm) \,\,sin\,\,(5t + 40x),$ where $‘t’$ is in seconds and $‘x’$ in meters, is sent along the lighter string towards the joint. The joint is at $x = 0$. The equation of the wave pulse reflected from the joint is
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 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 $100 ms^{^{-1}}$.