A) \[\left( \frac{{{v}^{2}}}{r}+a \right)\]
B) \[{{\left( \frac{{{v}^{2}}}{{{r}^{2}}}+a \right)}^{1/2}}\]
C) \[{{\left( \frac{{{v}^{4}}}{{{r}^{2}}}+{{a}^{2}} \right)}^{1/2}}\]
D) \[{{\left( \frac{{{v}^{2}}}{{{r}^{2}}}-{{a}^{2}} \right)}^{1/2}}\]
Correct Answer: C
Solution :
The car will have two accelerations, centripetal acceleration and tangential acceleration. Centripetal acceleration \[{{a}_{c}}=\frac{{{v}^{2}}}{r}\] (towards the centre) Tangential acceleration \[{{a}_{t}}=a\](along tangent) So, resultant acceleration \[A=\sqrt{a_{c}^{2}+a_{t}^{2}}\] \[A=\sqrt{\frac{{{v}^{4}}}{{{r}^{2}}}+{{a}^{2}}}\] \[A={{\left( \frac{{{v}^{4}}}{{{r}^{2}}}+{{a}^{2}} \right)}^{1/2}}\]
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