A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel through its centre. A small particle with negative charge, initially at rest far from the sphere, approaches it along the line

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Correct answer: D. 1.5 v

Potential at infinity =V_ ∞ =0 Potential at the surface of the sphere, V_s=k (Q)/(R) Potential at the centre of the sphere, V_c=(3)/(2) k (Q)/(R) 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. aligned & (1)/(2) m v^2=-q[V_ ∞ -V_s]=q k (Q)/(R) & (1)/(2) m v_0^2=-q[V_ ∞ -V_c]=q · (3)/(2) k (Q)/(R) aligned Dividing eqn. (ii) by eqn. (i), (v_0^2)/(v^2)=(3)/(2)=1.5 or v_0= 1.5 v

A large solid sphere with uniformly distributed positive charge has...

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