A) 2m
B) 1.5m
C) 1m
D) 0.5m
Correct Answer: B
Solution :
Key Idea: The kinetic energy of spring-ball system is conserved. Let spring is compressed by a length \[x\]. Kinetic energy of ball = Potential energy of spring i.e., \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}k{{x}^{2}}\] Given\[m=2\,kg,\,v=3\,m/s,\,k=144\,N/m\] \[\therefore \] \[\frac{1}{2}\times 2\times {{(3)}^{2}}=\frac{1}{2}\times 144\times {{x}^{2}}\] or \[9=72\,{{x}^{2}}\] \[\therefore \] \[x=\sqrt{\frac{9}{72}}=\frac{1}{2\sqrt{2}}m\] Hence, length of compressed spring \[=2-\frac{1}{2\sqrt{2}}\] \[=\frac{4\sqrt{2}-1}{2\sqrt{2}}\] = 1.5 m
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