GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 58 of 65

Marks: +1, -0

The

2 {kg}

block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness

5 {N} {/} {m}

The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity v of

1.5

m/s perpendicular to the cord. The magnitude of velocity in m\/s of the block at the instant the cord is stretched by

0.4

m is

Solution:

{m}=2 {kg}

{k}=5 {N} {/} {m}

By applying energy balance

\;{1}/{2} m v_{i}^{2}=\;{1}/{2} m v_{f}^{2}+\;{1}/{2} k x^{2}

\;\; =2 ×(1.5)^{2}=2 × v^{2} f+5 ×(.4)^{2}

V_{b}=1.360 {m} {/} {s}

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