Question

#PHYSICS

Q. A charged ball of mass m is performing vertical circular motion of radius l in a region where a uniform vertical upward electric field is present, what will be the minimum speed of ball at lowest point?

#Explain your answer properly​

Answer 1

A charged ball of mass m is performing vertical circular motion of radius l in a region where a uniform vertical upward electric field is present.

so, acceleration due to electric field, a = qE/m (upward )

at highest point ,

T + mg - ma = mv²/l

for just completing the circle , T = 0

so, mg - ma = mv²/l

or, v = √(g - a)l ......(1)

hence, at highest point, velocity of ball will be √(g - a)l.

now applying law of conservation of energy to find velocity of ball at lowest point.

energy at highest point = energy at lowest point

or, 1/2mv² + m(g - a)(2l) = 1/2mv'² [ actually net acceleration acting downward direction is (g - a) , that's why potential energy = m(g - a)l ]

or, v² + 4m(g - a)l = mv'²

from equation (1),

or, (g - a)l + 4(g - a)l = v'²

or, v' = √{5(g - a)l}

= $\sqrt{5\left(g-\frac{qE}{m}\right)l}$