(B) Given: Mass $m = 4\, kg$,extension $x_1 = 2\, cm = 0.02\, m$,final extension $x_2 = 5\, cm = 0.05\, m$,$g = 9.8\, m/s^2$.First,find the spring con

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(B) Given: Mass $m = 4\, kg$,extension $x_1 = 2\, cm = 0.02\, m$,final extension $x_2 = 5\, cm = 0.05\, m$,$g = 9.8\, m/s^2$.First,find the spring constant $K$ using Hooke's law: $F = Kx_1 \implies mg = Kx_1$.$K = \frac{mg}{x_1} = \frac{4 \times 9.8}{0.02} = \frac{39.2}{0.02} = 1960\, N/m$.The work done by an external agent to stretch the spring by $x_2$ is given by $W = \frac{1}{2} K x_2^2$.$W = \frac{1}{2} \times 1960 \times (0.05)^2$.$W = 980 \times 0.0025 = 2.45\, J$.

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

Medium

When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law,the spring stretches by $2\, cm$. The work required to be done by an external agent in stretching this spring by $5\, cm$ will be ......... $J$ $(g = 9.8\, m/s^2)$.

A
$4.90$
B
$2.45$
C
$0.495$
D
$0.245$

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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

$A$ 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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Two springs with spring constants $1500 \ N/m$ and $3000 \ N/m$ respectively are stretched by the same force. What is the ratio of their potential energies?

Medium

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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 with a force constant of $100 \ N/m$ is stretched by $5 \ cm$. Calculate the work done. (in $J$)

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$A$ spring has a spring constant $200 \,N/m$. If it is stretched by $1 \,cm$, then the potential energy stored in it is: (in $\,J$)

EasyAP EAMCET 2023

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When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law,the spring stretches by $2\, cm$. The work required to be done by an external agent in stretching this spring by $5\, cm$ will be ......... $J$ $(g = 9.8\, m/s^2)$.

Similar Questions

$A$ 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 .............. $J$.

Two springs with spring constants $1500 \ N/m$ and $3000 \ N/m$ respectively are stretched by the same force. What is the ratio of their potential energies?

$A$ 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 with a force constant of $100 \ N/m$ is stretched by $5 \ cm$. Calculate the work done. (in $J$)

$A$ spring has a spring constant $200 \,N/m$. If it is stretched by $1 \,cm$, then the potential energy stored in it is: (in $\,J$)

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