(B) The potential energy stored in the spring when it is compressed by an amount $x$ is given by $U = \frac{1}{2}kx^2$.Here,the natural length is $L_0

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$\sqrt {\frac{k}{m}} .\frac{{{L_0}}}{2}$

(B) The potential energy stored in the spring when it is compressed by an amount $x$ is given by $U = \frac{1}{2}kx^2$.Here,the natural length is $L_0$ and it is compressed to $L_0/2$,so the compression $x = L_0 - L_0/2 = L_0/2$.By the principle of conservation of mechanical energy,the potential energy stored in the spring is converted into the kinetic energy of the block when the spring returns to its natural length.$\frac{1}{2}mv^2 = \frac{1}{2}k\left(\frac{L_0}{2}\right)^2$$mv^2 = k\frac{L_0^2}{4}$$v^2 = \frac{k}{m} \cdot \frac{L_0^2}{4}$$v = \sqrt{\frac{k}{m}} \cdot \frac{L_0}{2}$

Class 11 Physics Work, Energy, Power and Collision Work Done by Spring and Potential Energy of Spring

Medium

$A$ block of mass $m$ is pushed against a spring with spring constant $k$,which is fixed at one end to a wall. The block can slide on a frictionless table as shown in the figure. If the natural length of the spring is $L_0$ and it is compressed to half its length when the block is released,find the velocity of the block when the spring reaches its natural length.

A
$\sqrt {\frac{m}{k}} .\frac{{{L_0}}}{2}$
B
$\sqrt {\frac{k}{m}} .\frac{{{L_0}}}{2}$
C
$\sqrt {\frac{k}{m}} .{L_0}$
D
$\sqrt {\frac{{k{L_0}}}{m}} $

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Class 11

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Work, Energy, Power and Collision

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Work Done by Spring and Potential Energy of Spring

The potential energy of a spring...

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$A$ block of mass $100 \ g$ moving at a speed of $2 \ m \ s^{-1}$ compresses a spring through a distance $2 \ cm$ before its speed is halved. Find the spring constant of the spring. (in $N \ m^{-1}$)

MediumTS EAMCET 2020

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$A$ spring of spring constant $200 \, Nm^{-1}$ is initially stretched by $10 \, cm$ from the unstretched position. The work to be done to stretch the spring further by another $10 \, cm$ is (in $J$)

EasyAP EAMCET 2024

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Two springs have their force constants as $k_1$ and $k_2$ $(k_1 > k_2)$. When they are stretched by the same force $F$,which of the following statements is true regarding the work done?

Medium

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An engine is attached to a wagon through a shock absorber of length $1.5 \, m$. The system with a total mass of $50,000 \, kg$ is moving with a speed of $36 \, km \, h^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest,the spring of the shock absorber gets compressed by $1.0 \, m$. If $90 \%$ of the energy of the wagon is lost due to friction,calculate the spring constant.

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The potential energy of a spring...

$A$ block of mass $100 \ g$ moving at a speed of $2 \ m \ s^{-1}$ compresses a spring through a distance $2 \ cm$ before its speed is halved. Find the spring constant of the spring. (in $N \ m^{-1}$)

$A$ spring of spring constant $200 \, Nm^{-1}$ is initially stretched by $10 \, cm$ from the unstretched position. The work to be done to stretch the spring further by another $10 \, cm$ is (in $J$)

Two springs have their force constants as $k_1$ and $k_2$ $(k_1 > k_2)$. When they are stretched by the same force $F$,which of the following statements is true regarding the work done?

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