A) \[{{G}^{1/2}}{{h}^{1/2}}{{c}^{-3/2}}\]
B) \[{{G}^{1/2}}{{h}^{1/2}}{{c}^{1/2}}\]
C) \[{{\left[ 2G\frac{({{m}_{1}}-{{m}_{2}}}{r} \right]}^{1/2}}\]
D) \[{{\left[ \frac{2G}{r}({{m}_{1}}+{{m}_{2}}) \right]}^{1/2}}\]
Correct Answer: B
Solution :
Key Idea Apply the principle of conservation of momentum and conservation of energy. Let velocities of these masses at r distance from each other be \[\Rightarrow \] and \[{{r}_{2}}=10m\] respectively. By conservation of momentum \[dl=Rd\theta \] \[dl=\lambda R\,d\theta \] \[\left\{ \lambda =\frac{q}{\pi R} \right\}\] ...(i) By conservation of energy Change in PE = change in KE \[dE=\frac{k.\lambda R\,d\theta }{{{R}^{2}}}\] \[dE\,\cos \theta ,\] \[dE\,sin\theta ,\] On solving Eqs. (i) and (ii) \[=2\int_{0}^{\pi /2}{dE\,\,\cos \theta }\] and \[=\frac{2k\lambda }{R}\int_{0}^{\pi /2}{\cos \theta \,d\theta }\] \[=\frac{2k\lambda }{R}\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{R}^{2}}}\] \[I=\frac{6}{2.8+1.2}=\frac{3}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
