(B) Let the extension in the length of the spring be $x$.The radius of the circular path is $r = 0.2 + x$.The centripetal force required for circular

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(B) Let the extension in the length of the spring be $x$.The radius of the circular path is $r = 0.2 + x$.The centripetal force required for circular motion is provided by the spring force (tension).$T = m \omega^2 r$$kx = m \omega^2 (0.2 + x)$Given $m = 100\,g = 0.1\,kg$,$k = 7.5\,N/m$,$\omega = 5\,rad/s$,and natural length $l_0 = 0.2\,m$.$7.5x = 0.1 \times (5)^2 \times (0.2 + x)$$7.5x = 0.1 \times 25 \times (0.2 + x)$$7.5x = 2.5 \times (0.2 + x)$$7.5x = 0.5 + 2.5x$$5x = 0.5$$x = 0.1\,m$The tension in the spring is $T = kx = 7.5 \times 0.1 = 0.75\,N$.

Class 11 Physics Newton's Laws of Motion and Friction Spring Force

Difficult

$A$ small block of mass $100\,g$ is tied to a spring of spring constant $7.5\,N/m$ and natural length $20\,cm$. The other end of the spring is fixed at a point $A$. If the block moves in a circular path on a smooth horizontal surface with a constant angular velocity of $5\,rad/s$ about point $A$,then the tension in the spring is $.........\,N$.

JEE MAIN 2023 All JEE MAIN

A
$1.5$
B
$0.75$
C
$0.25$
D
$0.50$

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Class 11

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Newton's Laws of Motion and Friction

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Spring Force

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Fill in the blank: The force constant of a spring is $0.5 \, Nm^{-1}$. The force necessary to increase the length of the spring by $10 \, cm$ will be .......... (in $, N$)

Easy

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Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is

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$A$ body of mass $m$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is $1 \, cm$. If the angular velocity is doubled,the elongation in the spring is $5 \, cm$. The original length of the spring is ............ $cm$.

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Two springs having spring constants $k_1$ and $k_2$ are connected in series,their resultant spring constant is $2 \text{ unit}$. If they are connected in parallel,their resultant spring constant is $9 \text{ unit}$. Find the values of $k_1$ and $k_2$.

Medium

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

Medium

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Fill in the blank: The force constant of a spring is $0.5 \, Nm^{-1}$. The force necessary to increase the length of the spring by $10 \, cm$ will be .......... (in $, N$)

Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is

Two springs having spring constants $k_1$ and $k_2$ are connected in series,their resultant spring constant is $2 \text{ unit}$. If they are connected in parallel,their resultant spring constant is $9 \text{ unit}$. Find the values of $k_1$ and $k_2$.

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