A ball of mass (1 ~g ) having a charge of (20 C ) is tied to one end of a string of length (0.9 ~m ) can rotate in a vertical plane in a uniform electric field (100 NC ⁻¹ ) directed upwards. The minimum horizontal velocity that must be given to the ball at the lowest position so that it completes the vertical circle is (Let, ( g =10 ~ms ⁻² ))

Step-by-step solution

Given, mass of ball, (m=1 ~g = 1 10^3 ~kg ) charge on the ball, (q=20 C=20 10⁻⁶ C ), length of the string centre of one end, (r=0.9 ~m ) electric field, (E=100 ~N / C ) and acceleration due to gravity, (g=10 ~m / s ^2 ) Now, according to the question, force exerted by the electric field due to charge on ball is given as, ( ) Force (= ) Charge on the ball ( ) Electric field ( aligned & F=q E F=20 10⁻⁶ 100 & F₁=2 10⁻³ ~N (i) aligned ) Now, force due to the gravitation, (F₂=m g= 1 10^3 10=10 10⁻³ ~N )...(ii) Net effec