A truck is pulling a car out of a ditch by means of a steel cable that is $9.1\,m$ long and has a radius of $5\,mm$, when the car just begins to move the tension in the cable is $800\,N$. How much has the cable stretched ? (Young’s modulus for steel is $ 2 \times 10^{11}\,Nm^{-2}$)
A truck is pulling a car out of a ditch by means of a steel cable that is $9.1\,m$ long and has a radius of $5\,mm$, when the car just begins to move the tension in the cable is $800\,N$. How much has the cable stretched ? (Young’s modulus for steel is $ 2 \times 10^{11}\,Nm^{-2}$)
$\mathrm{Y}=\frac{\mathrm{F} l}{\mathrm{~A} \Delta l}$
$\Delta l =\frac{\mathrm{F} l}{\mathrm{AY}}=\frac{\mathrm{F} l}{\pi r^{2} \mathrm{Y}}$
$\Delta l =\frac{800 \times 9.1}{3.14 \times\left(5 \times 10^{-3}\right)^{2} \times 2 \times 10^{11}}$
$=46.369 \times 10^{-5}$ $\approx 4.64 \times 10^{-4} \mathrm{~m}$
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- [JEE MAIN 2023]
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$(a)$ Find the distance $'y'$ from the top when the mass comes to rest for an instant, for the first time.
$(b)$ What is the maximum velocity attained by the stone in this drop ?
$(c)$ What shall be the nature of the motion after the stone has reached its lowest point ?
A stone is tied to an elastic string of negligible mass and spring constant $k$. The unstretched length of the string is $L$ and has negligible mass. The other end of the string is fixed to a nail at a point $P$. Initially the stone is at the same level as the point $P$. The stone is dropped vertically from point $P$.
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