A) 2.33 J
B) 8.67 J
C) 5.33 J
D) 6.67 J
Correct Answer: C
Solution :
From work-energy theorem kinetic energy of block at \[x=x\]is; \[K=\int_{0}^{x}{(4-{{x}^{2}})}.dx\] or \[K=4x-\frac{{{x}^{3}}}{3}\] For K to be maximum \[\frac{dK}{dx}=0\] or \[4-{{x}^{2}}=0\] or \[x=\pm 2\,m\] At \[x=+2\,m,\,\frac{{{d}^{2}}K}{d{{x}^{2}}}\]is negative i.e., kinetic energy (K) is maximum. \[\therefore \]\[{{K}_{\max }}=(4)(2)-\frac{{{(2)}^{2}}}{3}=\frac{16}{3}J\,=5.33\,J\] Hence, the correction option is (c).You need to login to perform this action.
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