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Q.

A simple pendulum with a bob of mass m=1kg, charge q=5μC and string length l=1m is given a horizontal velocity u in a uniform electric field E=2×106V/m at its bottommost point A, as shown in figure. It is given that the speed u is such that the particle leaves the circle at pint C. Find the speed u (Take g=10m/s2 )

A simple pendulum with a bob of mass m = 1 kg, charge q = 5muC and

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a

6 m / s

b

9 m / s

c

8 m / s

d

2 m / s

answer is C.

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Detailed Solution

 From work-energy theorem, 

A simple pendulum with a bob of mass m = 1 kg, charge q = 5muC and

12mv2-u2=-mg l 1+sin60°+qE l cos60°

 Substituting the values, we get

u2-v2=32.32

Further, at C tension in the string is zero.

Hence, mv2l=mgsin60°-qEcos60°

or   v2=3.66

...(ii)

From Eqs. (i) and (ii), we get

u=6m/s

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