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Two identical steel cubes (masses 50 g ,...

Two identical steel cubes (masses 50 g , side 1 cm ) collide head -on face to face with a space of 10 cm/s each . Find the maximum compression of each .Young's modulus for steel ` = Y = 2xx10^(11) N//m^(2)`

Text Solution

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Let m = 50 g = `50 xx 10^(-3)` kg
L = 1 cm = 0.01 m
v = 10 cm/s = 0.1 m/s
`Y = 2xx10^(11) N//m^(2)`
Here, KE will be converted to PE
`F = (YADeltaL)/l ` (Hooke.s Law )
` :. "Also " , F = DeltaL ` (K = spring constant)
` :. k = Y A/L = YL " " [ :. A =L^(2)] `
Intial `KE = 2xx 1/2 mv^(2) = 5xx10^(-4) J ` .
Final `PE = s xx 1/2 k(DeltaL)^(2) = k(DeltaL)^(2)`
` :. k(DeltaL)^(2) = 5xx10^(-4) = sqrt((5xx10^(-4))/(2xx10^(11)xx0.1))`
`= 1.58 xx10^(-7) m `
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