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  4. A body of mass 5 kg moving with a speed of 1.5 m / s on a horizontal smooth surface collides with a nearly weightless spring of force constant k=5 N / m . The maximum compression of the spring would be

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Q. A body of mass $5\, kg$ moving with a speed of $1.5\, m / s$ on a horizontal smooth surface collides with a nearly weightless spring of force constant $k=5\, N / \,m .$ The maximum compression of the spring would bePhysics Question Image

AIIMSAIIMS 2009

Solution:

At maximum compression the whole kinetic energy of ball = potential energy of spring.
$\frac{1}{2}mv^{2} = \frac{1}{2}kx^{2}$
$\Rightarrow x = v\sqrt{\frac{m}{k}}$
$x = 1.5\times\sqrt{\frac{5}{5}} = 1.5\,m$