(B) According to the law of conservation of energy,the potential energy lost by the block as it descends a vertical height $h$ is equal to the elastic

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(B) According to the law of conservation of energy,the potential energy lost by the block as it descends a vertical height $h$ is equal to the elastic potential energy gained by the spring at maximum compression $x$.The loss in gravitational potential energy of the block is $\Delta U_g = mgh$.The gain in elastic potential energy of the spring is $\Delta U_s = \frac{1}{2} Kx^2$.Equating the two:$mgh = \frac{1}{2} Kx^2$Solving for $x$:$x^2 = \frac{2mgh}{K}$$x = \sqrt{\frac{2mgh}{K}}$

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

Easy

$A$ block of mass $m$ slides down an inclined plane as shown in the figure and hits a spring at the bottom,causing it to compress. If the spring constant is $K$,what is the maximum compression of the spring?

A
$\sqrt {\frac{{mgh}}{k}} $
B
$\sqrt {\frac{{2mgh}}{k}} $
C
$\sqrt {\frac{{gh}}{{mk}}} $
D
$\sqrt {\frac{{2gh}}{{mk}}} $

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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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The force constants of two springs are $K_1$ and $K_2$. Both are stretched until their elastic potential energies are equal. If the stretching forces applied are $F_1$ and $F_2$,then the ratio $F_1:F_2$ is:

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The work done in stretching a spring of force constant $5 \times 10^3 \ N/m$ from $5 \ cm$ to $10 \ cm$ is ...... $N-m$.

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$Assertion$ : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.
$Reason$ : Potential energy of a stretched or compressed spring is proportional to the square of extension or compression.

EasyAIIMS 2017

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$A$ ball of mass $4\, kg$,moving with a velocity of $10\, ms^{-1}$,collides with a spring of length $8\, m$ and force constant $100\, Nm^{-1}$. The length of the compressed spring is $x\, m$. The value of $x$,to the nearest integer,is ........ .

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$A$ block of mass $m$ slides down an inclined plane as shown in the figure and hits a spring at the bottom,causing it to compress. If the spring constant is $K$,what is the maximum compression of the spring?

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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 .............. $J$.

The force constants of two springs are $K_1$ and $K_2$. Both are stretched until their elastic potential energies are equal. If the stretching forces applied are $F_1$ and $F_2$,then the ratio $F_1:F_2$ is:

The work done in stretching a spring of force constant $5 \times 10^3 \ N/m$ from $5 \ cm$ to $10 \ cm$ is ...... $N-m$.

$Assertion$ : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.$Reason$ : Potential energy of a stretched or compressed spring is proportional to the square of extension or compression.

$A$ ball of mass $4\, kg$,moving with a velocity of $10\, ms^{-1}$,collides with a spring of length $8\, m$ and force constant $100\, Nm^{-1}$. The length of the compressed spring is $x\, m$. The value of $x$,to the nearest integer,is ........ .

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$Assertion$ : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.
$Reason$ : Potential energy of a stretched or compressed spring is proportional to the square of extension or compression.