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, \[v=4m/s,m=16\,kg,k=100\,N/m\] \[\therefore \] \[x=4\times \sqrt{\frac{16}{100}}=1.6\,m\]
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