A) \[1.6\,\,m\]
B) \[4\,\,m\]
C) \[6.1\,\,m\]
D) \[3.2\,\,m\]
Correct Answer: A
Solution :
Kinetic energy of the block is \[K=\frac{1}{2}m{{v}^{2}}\] This kinetic energy is equal to the work done by the block before coming to rest. The work done in compressing the spring through a distance \[x\] from its normal length is \[W=\frac{1}{2}k{{x}^{2}}\] \[\therefore \] \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}k{{x}^{2}}\Rightarrow x=v\sqrt{\frac{m}{k}}\] Given,\[v=4\,\,m/s,\,\,m=16\,\,kg,\,\,k=100\,\,N/m\] \[\therefore \] \[x=4\times \sqrt{\frac{16}{100}}=1.6\,\,m\]
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