A) \[{{S}_{1}}={{S}_{2}}\]
B) \[{{S}_{1}}>{{S}_{2}}\]
C) \[{{S}_{1}}<{{S}_{2}}\]
D) Cannot say
Correct Answer: A
Solution :
Let \[{{m}_{1}},{{m}_{2}}\] be the masses and \[{{u}_{1}},{{u}_{2}}\] be the initial velocities of the truck and car respectively. As KE of both are equal, So, \[\frac{1}{2}{{m}_{1}}u_{1}^{2}=\frac{1}{2}{{m}_{2}}u_{2}^{2}\] or \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{u_{2}^{2}}{u_{1}^{2}}\] ?(i) As equal retarding force is applied on both then \[0=u_{1}^{2}-\frac{2f{{S}_{1}}}{{{m}_{1}}}\Rightarrow {{S}_{1}}=\frac{{{m}_{1}}u_{1}^{2}}{2f}\] And \[0=u_{2}^{2}-\frac{2f{{S}_{2}}}{{{m}_{2}}}\Rightarrow {{S}_{2}}=\frac{{{m}_{2}}u_{2}^{2}}{2f}\] So, \[\frac{{{S}_{1}}}{{{S}_{2}}}=\frac{{{m}_{1}}u_{1}^{2}}{{{m}_{2}}u_{2}^{2}}\]\[\therefore \frac{{{S}_{1}}}{{{S}_{2}}}=\frac{1}{1}\] or \[{{S}_{1}}={{S}_{2}}\]
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