A) \[{{(1.0002)}^{3000}}\]
B) \[(a.\hat{i})(a\times \hat{i})+(a.\hat{j})(a\times \hat{j})+(a.\hat{k})(a\times \hat{k})\]
C) \[A=\{(x,y):{{x}^{2}}+{{y}^{2}}=25\}\]
D) \[B=\{(x,y):{{x}^{2}}+{{y}^{2}}=144\};\]
Correct Answer: A
Solution :
Block of mass \[\frac{{{a}^{2}}}{{{(a+b)}^{2}}}\]shoots off carrying some kinetic energy away from the system. To find its speed, potential energy of spring = maximum kinetic energy of blocks. \[\frac{{{a}^{2}}}{{{b}^{2}}+{{(1-a)}^{2}}}\] [k = force constant of spring] \[\Delta ABC,\] with \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=ac+\sqrt{3}ab,\] along on the spring. Maximum potential energy = Maximum kinetic energy of \[(a\times b)\times c=\frac{1}{3}|b|\,\,|c|\] \[\theta \]\[\theta \] \[\frac{2\sqrt{2}}{3}\]\[\frac{\sqrt{2}}{3}\]
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