A) \[\frac{8}{9}J\]
B) \[\frac{12}{5}J\]
C) \[\frac{3}{7}J\]
D) \[\frac{11}{3}J\]
Correct Answer: A
Solution :
[a] \[{{U}_{1}} =\int\limits_{0}^{\ell /3}{-\frac{m}{\ell }gxdx=-\frac{1}{18}}mg\ell ;\] \[{{U}_{2}} =\int\limits_{0}^{\ell }{-\frac{m}{\ell }gxdx=-\frac{1}{2}}mg\ell ;\] \[loss in P.E. = {{U}_{1}}- {{U}_{2}} = \frac{4}{9} mg\ell \] \[=\frac{4}{9}\times 0.1\times 10\times 2=\frac{8}{9}J=Final\,\,K.E.\]
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