A) \[2.44m/{{s}^{2}}\]
B) \[4.9m/{{s}^{2}}\]
C) \[3.27m/{{s}^{2}}\]
D) \[3.5m/{{s}^{2}}\]
Correct Answer: D
Solution :
The linear acceleration of a ball which is rolling without slipping through an inclined plane with angle of inclination \[\theta \] is given by \[a=\frac{g\sin \theta }{\left( 1+\frac{{{K}^{2}}}{{{R}^{2}}} \right)}\] ?(i) (Given: \[g=9.8\,m/{{s}^{2}},\theta ={{30}^{o}}\]) Since, the value of \[\frac{{{K}^{2}}}{{{R}^{2}}}\] for solid ball is given by \[m{{K}^{2}}=\frac{2}{5}m{{R}^{2}}\] \[\therefore \] \[\frac{{{K}^{2}}}{{{R}^{2}}}=\frac{2}{5}\] Putting the given values in Eq. (i) \[a=\frac{9.8\times \sin {{30}^{0}}}{\left( 1+\frac{2}{5} \right)}=\frac{9.8\times 5}{2\times 7}=\frac{49}{14}=3.5\,m/{{s}^{2}}\]
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