InterviewSolution
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InterviewSolution
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A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel along its direction. A small particle with negative charge, initially at rest far from the sphere, approaches it along the line of the tunnel, reaches its surface with a speed `v`, and passes through the tunnel. Its speed at the centre of the sphere will be |
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Answer» Correct Answer - b Let `m` and `-q` be the mass and the charge of the particle respectively. Let `v_(0)=`speed of the particle at the centre of the sphere. Using conservation of mechanical energy `Delta K+Delta U=0` `((1)/(2)mv_(s)^(2)-0)+[-q(V_(s)-V_(oo))=0` `(1)/(2)mv_(s)^(2)=q[V_(s)-0]=qV_(S)` Similarly `(1)/(2)mv_(0)^(2)=q[V_(c )-0]=qV_(c )` We know `V_(c )=(3)/(2)k(Q)/(R)V_(s)=k(Q)/(R)` Hence `(1)/(2)mv_(s)^(2)=q.k(Q)/(R )`....(i) and `(1)/(2)mv_(0)^(2)=q(3)/(2)(Q)/(R)`....(ii) Dividing Eq. (ii) by (i), `(v_(0)^(2))/(v^(2)) = (3)/(2) =1.5` or `v_(0) = sqrt(1.5)v` |
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