(C) Case $(a)$: When stretched by the same amount $x$,the work done is $W = \frac{1}{2} K x^2$. Since $K_P > K_Q$ and $x$ is the same,$W_P = \frac{1}{

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(C) Case $(a)$: When stretched by the same amount $x$,the work done is $W = \frac{1}{2} K x^2$. Since $K_P > K_Q$ and $x$ is the same,$W_P = \frac{1}{2} K_P x^2$ and $W_Q = \frac{1}{2} K_Q x^2$. Therefore,$W_P > W_Q$.Case $(b)$: When stretched by the same force $F$,the work done is $W = \frac{F^2}{2K}$. Since $K_P > K_Q$ and $F$ is the same,$W_P = \frac{F^2}{2K_P}$ and $W_Q = \frac{F^2}{2K_Q}$. Since $K_P > K_Q$,it follows that $\frac{1}{K_P} W_P$.

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

Medium

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:

AIPMT 2015 All AIPMT

A
$W_P > W_Q, W_P < W_Q$
B
$W_P = W_Q, W_P = W_Q$
C
$W_P > W_Q, W_Q > W_P$
D
$W_P < W_Q, W_Q < W_P$

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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

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If a spring extends by $x$ on loading,then the energy stored by the spring is (if $T$ is tension in the spring and $k$ is spring constant).

MediumAIIMS 1997

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$A$ massless spring of force constant $K$ is placed between two blocks of masses $m$ and $M$ on a frictionless table and compressed by an amount $x$. Upon releasing the spring,both blocks move in opposite directions. The blocks lose contact with the spring when it reaches its natural length. The speed of the block of mass $M$ at the moment of separation is:

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The potential energy of a long spring when stretched by $2 \ cm$ is $U$. If the spring is stretched by $8 \ cm$,the potential energy stored in it is:

Medium

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$A$ mass of $1 \ kg$ falls from a height of $1 \ m$ and lands on a massless platform supported by a spring having spring constant $15 \ N \ m^{-1}$ as shown in the figure. The maximum compression of the spring is. (acceleration due to gravity $= 10 \ m \ s^{-2}$)

DifficultAP EAMCET 2022

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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:

Similar Questions

If a spring extends by $x$ on loading,then the energy stored by the spring is (if $T$ is tension in the spring and $k$ is spring constant).

The potential energy of a long spring when stretched by $2 \ cm$ is $U$. If the spring is stretched by $8 \ cm$,the potential energy stored in it is:

$A$ mass of $1 \ kg$ falls from a height of $1 \ m$ and lands on a massless platform supported by a spring having spring constant $15 \ N \ m^{-1}$ as shown in the figure. The maximum compression of the spring is. (acceleration due to gravity $= 10 \ m \ s^{-2}$)

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