A) \[\frac{1}{8}m{{a}^{4}}{{t}^{2}}\]
B) \[4m{{a}^{4}}{{t}^{2}}\]
C) \[8m{{a}^{4}}{{t}^{2}}\]
D) \[\frac{1}{4}m{{a}^{4}}{{t}^{2}}\]
Correct Answer: A
Solution :
| [a] Velocity of body |
| \[v=a\sqrt{s}\] |
| acceleration\[a'=\frac{dv}{dt}=\frac{a}{2\sqrt{s}}\frac{ds}{dt}=\frac{{{a}^{2}}}{2}\] |
| displacement\[s'=\frac{1}{2}a'{{t}^{2}}=\frac{1}{2}\frac{{{a}^{2}}}{2}{{t}^{2}}\] |
| Work done\[W=force\times displacement\] |
| \[W=ma'\times s'=\frac{1}{8}m{{a}^{4}}{{t}^{2}}\] |
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