A) 8.5 cm
B) 5.5 cm
C) 2.5 cm
D) 11.0 cm
Correct Answer: B
Solution :
[b] Let the blow compress the spring by x before stopping. Kinetic energy of the block = (P.E of compressed spring) + work done against function. \[\frac{1}{2}\times 2\times {{\left( 4 \right)}^{2}}=\frac{1}{2}\times 10,000\times {{x}^{2}}+\left( +15 \right)\times x\] \[10,000{{x}^{2}}+30x-32=0\] \[\Rightarrow 5,000{{x}^{2}}+15x-16=0\] \[\therefore \,\,\,x=-\frac{15\pm \sqrt{{{\left( 15 \right)}^{2}} \pm - 4\times (5000)(-16)}}{2\times 5000}\] \[=0.055\text{ }m=5.5\text{ }cm.\]
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