A) \[\frac{5}{7}g\,\sin \,\theta \]
B) \[\frac{3}{7}g\,\sin \,\theta .\]
C) \[\frac{2}{7}g\,\sin \,\theta .\]
D) \[\frac{2}{5}g\,\sin \,\theta .\]
Correct Answer: A
Solution :
Acceleration of the sphere \[a=\frac{g\sin \theta }{1+\frac{{{k}^{2}}}{{{r}^{2}}}}=\frac{g\sin \theta }{1+\frac{2}{5}}\] \[\left[ \because For\text{ }sphere\frac{{{k}^{2}}}{{{r}^{2}}}=\frac{2}{5} \right]\] \[=\frac{5}{7}g\sin \theta \]
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