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5.Work, Energy, Power and Collision
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The figure shows a mass $m$ on a frictionless surface. It is connected to rigid wall by the mean of a massless spring of its constant $k$. Initially, the spring is at its natural position. If a force of constant magnitude starts acting on the block towards right, then the speed of the block when the deformation in spring is $x,$ will be
A
$\sqrt{\frac{2 F{x}-k x^{2}}{m}}$
B
$\sqrt{\frac{F{x}-k x^{2}}{m}}$
C
$\sqrt{\frac{x(F-k)}{m}}$
D
$\sqrt{\frac{F{x}-k x^{2}}{2 m}}$
(AIIMS-2018)
Solution
Free body diagram of block is shown below.
Now, from the energy conservation,
$w=\Delta K$
$w_{F}+w_{s p}=\frac{1}{2} m v^{2}-0$
$\Rightarrow F_{x}-\frac{1}{2} k x^{2}=\frac{1}{2} m v^{2}$
$\therefore v=\sqrt{\frac{2 F_{x}-k x^{2}}{m}}$
Standard 11
Physics
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