A) 200 m
B) 16 am
C) 80 m
D) 40 m
Correct Answer: C
Solution :
Initial height of the body\[{{h}_{1}}=20\,m\] Initial mass of the first body \[{{m}_{1}}=m\] Final mass of the body\[{{m}_{2}}=2\,m\] Final velocity \[=2\,\upsilon \] The equation of motion for maximum heights \[{{\upsilon }^{2}}={{u}^{2}}-2gh\] or \[0={{u}^{2}}-2gh\] or \[2gh={{u}^{2}}\] or \[h\propto {{u}^{2}}\] Hence \[\frac{{{h}_{1}}}{{{h}_{2}}}={{\left( \frac{{{u}_{1}}}{{{u}_{2}}} \right)}^{2}}\] \[\frac{{{h}_{1}}}{{{h}_{2}}}=\left( \frac{u}{2u} \right)=\frac{1}{4}\] or \[{{h}_{2}}=4h=4\times 20=80\,m\]
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