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Question

# A mass of 2 kg falls from a height of 40 cm on a spring of force constant 1960 N/m. The spring is compressed by:

A
10 cm
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B
0.4 cm
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C
0.01 cm
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D
0.04 cm
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Solution

## The correct option is A 10 cmGiven,Mass=2kg,height=40cm Force constant k=1960N/mLet the h be the height from which the mass m falls on the spring of the force constant k and x is the compression on the string.So, the gain in the elastic potential energy of string is equal to the loss in gravitational potential energy of falling mass,12kx2=mg(h+x)⇒121960×x2=2×9.8(0.40+x)⇒980x2=7.84+19.6x⇒980x2−19.6x−7.84=0 x=10 cm

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