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5.Work, Energy, Power and Collision
hard
A ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$ . Other end of spring is fixed and ring can slide on a smooth horizontal rod as shown. Now the ring is shifted to position $B$ and released, speed of ring when spring attains it's natural length is
A
$\frac{{2{l_0}}}{3}\sqrt {\frac{k}{m}} $
B
$\frac{{{l_0}}}{3}\sqrt {\frac{k}{m}} $
C
$\frac{{3{l_0}}}{2}\sqrt {\frac{k}{m}} $
D
${l_0}\sqrt {\frac{k}{m}} $
Solution
$\cos 53^{\circ}=\frac{\ell_{0}}{\ell_{0}+\mathrm{x}}$
$\frac{3}{5}=\frac{\ell_{0}}{\ell_{0}+\mathrm{X}}$
$\mathrm{x}=\frac{2}{3} \ell_{0}$
from $\mathrm{B} \rightarrow \mathrm{A}$
$\frac{1}{2} \mathrm{kx}^{2}=\frac{1}{2} \mathrm{mv}^{2}$
$v=x \sqrt{\frac{k}{m}}=\frac{2}{3} \ell_{0} \sqrt{\frac{k}{m}}$
Standard 11
Physics
