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Question

A disc of mass 3m and a disc of mass m are connected by a massless spring of stiffness k.The heavier disc is placed on the ground with the spring vertical and lighter disc on top. From its equilibrium position the upper disc is pushed down by a distance δ and released.Then

A
if δ>3mgk, the lower disc will bounce up
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B
if δ>2mgk, maximum normal reaction from ground on lower disc=6mg
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C
if δ>2mgk, maximum normal reaction from ground on lower disc=4mg
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D
if δ>4mgk, the lower disc will bounce up
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Solution

The correct options are
B if δ>2mgk, maximum normal reaction from ground on lower disc=6mg
D if δ>4mgk, the lower disc will bounce up
(a) At equilibrium
kδ0=mg or δ0=mgk
where δ0=compression
(b)δTotal=δ+δ0=3mgk
Fmax=kδmax=k(3mgk)=3mg
Nmax=3mg+Fmax=6mg
134620_119607_ans.png

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