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  4. Consider the situation shown in figure. A spring of spring constant 400 N / m is attached at one end to a wedge fixed rigidly with the horizontal part. A 40 g mass is released from rest while situated at a height 5 cm the curved track. The minimum deformation in the spring is nearly equal to (take g=10 m / s 2 )

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Q. Consider the situation shown in figure. A spring of spring constant $400\, N / m$ is attached at one end to a wedge fixed rigidly with the horizontal part. A $40\, g$ mass is released from rest while situated at a height $5\, cm$ the curved track. The minimum deformation in the spring is nearly equal to (take $g=10\, m / s ^{2}$ )Physics Question Image

AIIMSAIIMS 2015

Solution:

Applying the conservation of momentum to the system
$m g h=\frac{1}{2} k x^{2}$
Given, $m=0.04 \,kg , h=5 \,m , K=400 \,N / m$
and $x=$ deformation (compression) in the spring
$\Rightarrow x =\sqrt{\frac{2 m g h}{k}}=\sqrt{\frac{2 \times 0.04 \times 10 \times 5}{400}} $
$=\frac{1}{10} m =10 \,cm \approx 9.8\, cm$