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5.Work, Energy, Power and Collision
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Two blocks of mass $2\ kg$ and $1\ kg$ are connected by an ideal spring on a rough surface. The spring in unstreched. Spring constant is $8\ N/m$ . Coefficient of friction is $μ = 0.8$ . Now block $2\ kg$ is imparted a velocity $u$ towards $1\ kg$ block. Find the maximum value of velocity $'u'$ of block $2\ kg$ such that block of $1\ kg$ mass never move is

A
$\sqrt {10}\ m/s$
B
$\sqrt {15}\ m/s$
C
$\sqrt {20}\ m/s$
D
$\sqrt {30}\ m/s$
Solution

$\mathrm{kx}=\mu \mathrm{mg}$
$8 x=0.8 \times 1 \times 10$
$x=1$
$+\frac{1}{2} k x^{2}+\mu m g x-0+\frac{1}{2} m v^{2}$
$\frac{1}{2} \times 8 \times 1^{2}+0.8 \times 2 \times 10 \times 1=\frac{1}{2} \times 2 \times u^{2}$
$4+16=u^{2}$
$\mathrm{u}=\sqrt{20} \mathrm{m} / \mathrm{s}$
Standard 11
Physics
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