1no one
a particle of mass 1 kg n charge 1/3 microc is projected towards a non conducting fixed spherical shell having the same charge uniformly distributed on its surface .radius of shell is 1 mm .distance b/w the line of motion n line containing the centre of shell is .5 mm .assume the partice to be cming frm infinity.find minimum initial velocity of projection if the particle grazes the shell
(a)√2/√3
(b)2√2/√3
(c)2/3
(d)none
all velocities are in m/s
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6 Answers
66System: the two charges. No external torque about the center of fixed sphere. Accordingly, the angular momentum about the center remains constant. So, we have
mv_0R/2 = mvR
giving the speed with which it grazes the sphere as v=v_0/2. Here, v_0 is the initial speed of project.
Since the system is closed, the mechanical energy remains constant. Hence,
\dfrac{1}{2}mv_0^2=\dfrac{1}{2}mv^2 +\dfrac{1}{4\pi\epsilon_0}\dfrac{q^2}{R}
Using v=v_0/2 and solving for v_0 give us
v_0=\sqrt{\dfrac{8}{3}\cdot\dfrac{q^2}{4\pi\epsilon_0 mR}}
Plugging the relevant values, we get v_0=\sqrt{\dfrac{8}{3}} m/s. Hence, option (b) is correct.