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
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]
- 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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Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.
Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.
- [AIIMS 2019]
$A$ small block of mass $m$ is placed on $a$ wedge of mass $M$ as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down, then Maximum velocity of $M$ is:
$A$ small block of mass $m$ is placed on $a$ wedge of mass $M$ as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down, then Maximum velocity of $M$ is:
In a spring gun having spring constant $100\, {N} / {m}$ a small ball $'B'$ of mass $100\, {g}$ is put in its barrel (as shown in figure) by compressing the spring through $0.05\, {m}$. There should be a box placed at a distance $'d'$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of $2\, {m}$ above the ground. The value of $d$ is $....{m} .$ $\left(g=10\, {m} / {s}^{2}\right)$
In a spring gun having spring constant $100\, {N} / {m}$ a small ball $'B'$ of mass $100\, {g}$ is put in its barrel (as shown in figure) by compressing the spring through $0.05\, {m}$. There should be a box placed at a distance $'d'$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of $2\, {m}$ above the ground. The value of $d$ is $....{m} .$ $\left(g=10\, {m} / {s}^{2}\right)$
- [JEE MAIN 2021]
This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement $-1$: If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$
Statement $-2$ : $k_1 < k_2$.
This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement $-1$: If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$
Statement $-2$ : $k_1 < k_2$.
A uniform solid cylinder of mass $M = 3\ kg$ and radius $R = 10\ cm$ is connected about an axis through the cnetre of the cylinder to a horizontal spring with spring constant $8\ N/m$.The cylinder is pulled back, stretching the spring $1\,m$ from equilibrium.When released, the cylinder rolls without slipping. What is the speed of the center of th ecylinder when it returns to equilibrium? .................. $m/s$
A uniform solid cylinder of mass $M = 3\ kg$ and radius $R = 10\ cm$ is connected about an axis through the cnetre of the cylinder to a horizontal spring with spring constant $8\ N/m$.The cylinder is pulled back, stretching the spring $1\,m$ from equilibrium.When released, the cylinder rolls without slipping. What is the speed of the center of th ecylinder when it returns to equilibrium? .................. $m/s$