A) \[k\,{{r}^{2}}\,{{t}^{2}}\]
B) \[{{k}^{2}}\,{{r}^{2}}\,t\]
C) \[{{k}^{2}}\,r\,{{t}^{2}}\]
D) \[k\,\,{{r}^{2}}t\]
Correct Answer: C
Solution :
\[p=m{{K}^{2}}{{r}^{2}}t=m{{a}_{t}}v\] \[{{a}_{t}}\,v={{K}^{2}}r\] \[v\frac{dv}{dt}\,={{K}^{2}}\,{{r}^{2}}t\] \[\frac{{{v}^{2}}}{2}\,=\frac{{{K}^{2}}{{r}^{2}}{{t}^{2}}}{2}\,\,or\,\,v=krt\] \[{{a}_{T}}\,=\frac{dv}{dt}\,=kr\] So \[{{a}_{c}}=\frac{{{v}^{2}}}{r}\,={{k}^{2}}r{{t}^{2}}\]
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