A) \[{{s}_{2}}=2{{s}_{1}}\]
B) \[{{s}_{2}}=\frac{{{s}_{1}}}{2}\]
C) \[{{s}_{2}}={{s}_{1}}\]
D) \[{{s}_{2}}=4{{s}_{1}}\]
Correct Answer: D
Solution :
: By applying constant retarding force F the body is brought to rest so \[\upsilon =0\]. Retardation, \[a=-\frac{F}{m}\] If s be distance travelled by the body before it comes to rest (called stopping distance). Using 3rd equation of motion \[{{\upsilon }^{2}}-{{\upsilon }^{2}}=2as\] \[{{(0)}^{2}}-{{u}^{2}}=2\left( -\frac{F}{m}s \right)\] \[s=\frac{{{u}^{2}}m}{2F}\] \[s\propto {{u}^{2}}\]For the same of m.F. \[\therefore \] \[\frac{{{s}_{1}}}{{{s}_{2}}}={{\left( \frac{u}{2u} \right)}^{2}}=\frac{1}{4}\] or \[{{s}_{2}}=4{{s}_{1}}\]
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