A) \[\text{3}.0\text{ m}/{{\text{s}}^{\text{2}}}\]
B) \[\text{2}.\text{7 m}/{{\text{s}}^{\text{2}}}\]
C) \[\text{1}.\text{8 m}/{{\text{s}}^{\text{2}}}\]
D) \[\text{2}.\text{5 m}/{{\text{s}}^{\text{2}}}\]
Correct Answer: B
Solution :
Radial acceleration due to circular path, \[{{a}_{r}}=\frac{{{v}^{2}}}{r}=\frac{{{(30)}^{2}}}{500}=\frac{9}{5}=1.8\,\,m/{{s}^{2}}\] Tangential acceleration due to increase in tangential speed \[{{a}_{t}}=\frac{\Delta v}{\Delta t}=2\,\,m/{{s}^{2}}\] \[\therefore \]Net acceleration, \[{{a}_{t}}=\sqrt{{{a}_{r}}^{2}+{{a}_{t}}^{2}}\] \[=\sqrt{{{(1.8)}^{2}}+{{(2)}^{2}}}\] \[=\mathbf{2}\mathbf{.7}\,\,\mathbf{m/}{{\mathbf{s}}^{\mathbf{2}}}\]
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