One end of a massless spring of spring constant k and natural length l

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4-1.Newton's Laws of Motion

medium

One end of a massless spring of spring constant $k$ and natural length $l_{0}$ is fixed while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be

A$\frac{ k - m \omega^{2} l_{0}}{ m \omega^{2}}$

B$\frac{ m \omega^{2} l_{0}}{ k + m \omega^{2}}$

C$\frac{ m \omega^{2} l_{0}}{ k - m \omega^{2}}$

D$\frac{ k + m \omega^{2}l_{0}}{m \omega^{2}}$

(JEE MAIN-2022) (JEE MAIN-2020)

Solution

$K \Delta x = m \left(\ell_{0}+\Delta x \right) w ^{2}$
$K \Delta x = m \ell_{0} w ^{2}+ mw ^{2} \Delta x$
$\Delta x =\frac{ m \ell_{0} w ^{2}}{ k – mw ^{2}}$

Standard 11

Physics

Natural length of a spring is $60\, cm$, and its spring constant is $4000\, N/m$. A mass of $20\, kg$ is hung from it. The extension produced in the spring is,…….$cm$ (Take $g = 9.8\;m/{s^2}$)

easy

In the figure, blocks $A$ and $B$ of masses $2m$ and $m$ are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses $2m$ and $m$ just after the instant when the string is cut

medium

(AIIMS-2018)

The masses of $10\, kg$ and $20 \,kg$ respectively are connected by a massless spring as shown in figure. A force of $200\, N$ acts on the $20\, kg$ mass. At the instant shown, the $10\, kg$ mass has acceleration $12\,m/{\sec ^2}$. What is the acceleration of $20\, kg$ mass ……….. $m/{\sec ^2}$

medium

Two blocks $A$ and $B$ of masses $3\,m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively

medium

(NEET-2017)

In the figure given below, what is the reading of the balance ? (Take $g = 10\, N \,kg^{-1})$ ………… $N$

easy

Solution

Similar Questions

Natural length of a spring is $60\, cm$, and its spring constant is $4000\, N/m$. A mass of $20\, kg$ is hung from it. The extension produced in the spring is,…….$cm$ (Take $g = 9.8\;m/{s^2}$)

In the figure, blocks $A$ and $B$ of masses $2m$ and $m$ are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses $2m$ and $m$ just after the instant when the string is cut

Two blocks $A$ and $B$ of masses $3\,m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively

In the figure given below, what is the reading of the balance ? (Take $g = 10\, N \,kg^{-1})$ ………… $N$

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