(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 and Power 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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Chapter

Work, Energy and Power

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Work Done by Spring and Potential Energy of Spring

When equal forces are applied to two springs with spring constants $1500 \, N/m$ and $3000 \, N/m$,what is the ratio of their stored potential energies?

Medium

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Two similar springs $P$ and $Q$ have spring constants $K_P$ and $K_Q$,such that $K_P > K_Q$. They are stretched first by the same amount (case $a$),then by the same force (case $b$). The work done by the springs $W_P$ and $W_Q$ are related as,in case $(a)$ and case $(b)$ respectively:

MediumAIPMT 2015

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Statement-$1$ and Statement-$2$ are given. Two springs $S_1$ and $S_2$ have force constants $k_1$ and $k_2$ respectively,where $k_1 < k_2$. They are stretched by the same force $F$. It is found that the work done on spring $S_1$ is greater than the work done on spring $S_2$.
Statement-$1$: If stretched by the same force,the work done on $S_1$ is greater than the work done on $S_2$.
Statement-$2$: $k_1 < k_2$.

Easy

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If a spring extends by $x$ on loading,then the energy stored in the spring is (where $T$ is the tension in the spring and $K$ is the spring constant):

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$A$ spring of spring constant $5 \times 10^3 \, N/m$ is stretched initially by $5 \, cm$ from the unstretched position. Then the work required to stretch it further by another $5 \, cm$ is .............. $J$.

MediumAIEEE 2003

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Similar Questions

When equal forces are applied to two springs with spring constants $1500 \, N/m$ and $3000 \, N/m$,what is the ratio of their stored potential energies?

Two similar springs $P$ and $Q$ have spring constants $K_P$ and $K_Q$,such that $K_P > K_Q$. They are stretched first by the same amount (case $a$),then by the same force (case $b$). The work done by the springs $W_P$ and $W_Q$ are related as,in case $(a)$ and case $(b)$ respectively:

If a spring extends by $x$ on loading,then the energy stored in the spring is (where $T$ is the tension in the spring and $K$ is the spring constant):

$A$ spring of spring constant $5 \times 10^3 \, N/m$ is stretched initially by $5 \, cm$ from the unstretched position. Then the work required to stretch it further by another $5 \, cm$ is .............. $J$.

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