(D) The potential energy $U$ of a spring is given by the formula $U = \frac{1}{2} K x^2$,where $K$ is the spring constant and $x$ is the extension or

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If the $Assertion$ is incorrect but $Reason$ is correct.

(D) The potential energy $U$ of a spring is given by the formula $U = \frac{1}{2} K x^2$,where $K$ is the spring constant and $x$ is the extension or compression.This equation shows that $U \propto x^2$.The graph of $U$ versus $x$ represents a parabola,not a straight line.Therefore,the $Assertion$ is incorrect because the relationship is quadratic,not linear.The $Reason$ is correct because it correctly states that the potential energy is proportional to the square of the extension or compression $(U \propto x^2)$.

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

Easy

$Assertion$ : 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.

AIIMS 2017 All AIIMS

A
If both $Assertion$ and $Reason$ are correct and the $Reason$ is a correct explanation of the $Assertion$.
B
If both $Assertion$ and $Reason$ are correct but $Reason$ is not a correct explanation of the $Assertion$.
C
If both the $Assertion$ and $Reason$ are incorrect.
D
If the $Assertion$ is incorrect but $Reason$ is correct.

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Class 11

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Chapter

Work, Energy, Power and Collision

Subtopic

Work Done by Spring and Potential Energy of Spring

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AIIMS 2017 Paper All AIIMS years →

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

Easy

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$A$ spring with a force constant of $800 \ N/m$ is stretched by $5 \ cm$. Find the work done in stretching it from $5 \ cm$ to $15 \ cm$ in $J$.

Difficult

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An ideal spring with spring constant $k$ is suspended from the ceiling,and a block of mass $M$ is attached to its lower end. Initially,the spring is unstretched and the block is released from rest. What will be the maximum extension in the spring?

Difficult

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$A$ block of mass $m=25 \ kg$ sliding on a smooth horizontal surface with a velocity $v=3 \ ms^{-1}$ meets a spring of spring constant $k=100 \ N/m$ fixed at one end as shown in the figure. The maximum compression of the spring and the velocity of the block as it returns to the original position are, respectively:

DifficultTS EAMCET 2007

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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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$Assertion$ : 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.

Similar Questions

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

$A$ spring with a force constant of $800 \ N/m$ is stretched by $5 \ cm$. Find the work done in stretching it from $5 \ cm$ to $15 \ cm$ in $J$.

An ideal spring with spring constant $k$ is suspended from the ceiling,and a block of mass $M$ is attached to its lower end. Initially,the spring is unstretched and the block is released from rest. What will be the maximum extension in the spring?

$A$ 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 $J$)

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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.