A) \[1.25\,x\]
B) \[x\]
C) \[5x\]
D) \[2.5x\]
Correct Answer: A
Solution :
From equation of motion \[{{v}^{2}}={{u}^{2}}+2as\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,{{v}^{2}}-{{u}^{2}}=-2\,\left( \frac{F}{m} \right)\] \[-{{u}^{2}}=-\,\frac{F}{m}.\,s\Rightarrow \,{{u}^{2}}=\frac{2F.s}{m}\] or \[m=\frac{2F.s}{{{u}^{2}}}\Rightarrow \,m\propto s\]given, \[{{s}_{1}}=x,\,\,{{s}_{2}}=?\] \[{{m}_{1}}=m\] \[{{m}_{2}}=m\times 25%\,+m\] Now, \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{s}_{1}}}{{{s}_{2}}}\] \[\frac{m}{m\times \frac{25}{100}+m}\,=\frac{x}{{{s}_{2}}}\] \[{{s}_{2}}=\frac{x\times m\left( \frac{100+25}{100} \right)}{m}\,=\frac{125}{100}x\Rightarrow \,{{s}_{2}}=1.25\,x\]
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