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A block movig horizontally ona smooth su...

A block movig horizontally ona smooth surace with a speed of 20 m/s bursts into thwo equal parts cobtinuing in the same direction. If one of the parts moves at 30 m/s, with whast speed does the second part move and what is tehfractional change in the kinetic energy?

Text Solution

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There is no exterN/Al force on the block. InterN/Al forces break the block in two parts. The liear momentum of the block befoe the break shuld therefore be equal to tehlinear momentum of the wo parts after the break. As all thevelocities are in same directin we get
`M(20 m/s)=M/2(30m/s)+M/2v`
where v is th speed of the other part. From this equation `v=10m/s.` The change in kinetic energy is `1/2M/2(3m/s)^2+1/2 M/2(10m/s)^2-1/2M(20m/s)^2`
`=m/(450+50-40) m^2/s^2=(50 m^2/s^2)M`.
`Hence the fractioN/Al change in the kinetic energy
`(M(50 m^2/s^2))/(1/2M(20m/s)^2)=1/4`
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