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Q.

A positively charged particle of charge q and mass m is suspended from a point by a string of length l in a vertical plane. In the entire space a uniform horizontal electric field E exists. The particle is drawn aside so that string becomes vertical and then particle is projected horizontally with velocity v such that particle starts to move along a circle with some constant speed v. Then choose the correct statements.

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a

Tension in the string is mg+q2E2mg

b

Time period of revolution is independent of mass of particle.  

c

Time period of revolution is  2πlgg2+(qEm)2

d

Speed of the particle is v=qEmlg

answer is A, B, C.

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Detailed Solution

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geff=g2+(qEm)2 Tcosθ=mgeff Tcosθ=mRω2 Rω2geff=tanθ ω2=gefftanθlsinθgefflcosθ ω=gefflcosθ cosθ=Igeff sinθ=qEmgeff

Time period 2πω2πgefflg2πlgg2+(qEm)2

vRwlsinθgefflcosθ v=lqEmgeff.g2efflg v=qEm.lg T=mg2effgmg[g2+(qEm)2] T=[mg+q2E2mg]

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A positively charged particle of charge q and mass m is suspended from a point by a string of length l in a vertical plane. In the entire space a uniform horizontal electric field E exists. The particle is drawn aside so that string becomes vertical and then particle is projected horizontally with velocity v such that particle starts to move along a circle with some constant speed v. Then choose the correct statements.