A) 2
B) 4
C) 6
D) 8
Correct Answer: D
Solution :
It is clear from figure that the displacement vector \[\Delta \overrightarrow{r}\] between particles \[{{p}_{1}}\] and \[{{p}_{2}}\] is \[\Delta \overrightarrow{r}=\overrightarrow{{{r}_{2}}}-\overrightarrow{{{r}_{1}}}=-8\hat{i}-8\hat{j}\] \[|\Delta \overrightarrow{r}|\,=\sqrt{{{(-8)}^{2}}+{{(-8)}^{2}}}=8\sqrt{2}\] ?..(i) Now, as the particles are moving in same direction \[(\because \ \overrightarrow{{{v}_{1}}}\text{ and }\overrightarrow{{{v}_{2}}}\text{ are }+ve)\], the relative velocity is given by \[{{\overrightarrow{v}}_{rel}}=\overrightarrow{{{v}_{2}}}-\overrightarrow{{{v}_{1}}}=(\alpha -4)\hat{i}+4\hat{j}\] \[{{\overrightarrow{v}}_{rel}}=\sqrt{{{(\alpha -4)}^{2}}+16}\] ?..(ii) Now, we know \[|{{\overrightarrow{v}}_{rel}}|\,=\frac{|\Delta \overrightarrow{r}|}{t}\] Substituting the values of \[{{\overrightarrow{v}}_{rel}}\] and \[|\Delta \overrightarrow{r}|\] from equation (i) and (ii) and \[t=2s\], then on solving we get \[\alpha =8\]You need to login to perform this action.
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