A particle ' A ' has charge ' +q ' and a particle ' B '. has charge ' +4 q '. Each has same mass ' m '. When they are allowed to fall from rest through the same potential, the ratio of their speeds will become (particle A to particle B)

Step-by-step solution

Electric force on charged particle placed in a electric field. aligned & F=q E & F_A=+q E & F_A=m_A a_A a_A & = q E m F_B & =+4 q E F_B & =m_B a_B & a_B= 4 q E m & a_A= a_B 4 ...(i) aligned As both the bodies are falling from rest and cover same distance. aligned & V_A^2=0+2 a_A x & V_B^2=0+2 a_B x aligned array ll ( V_A V_B )^2= a_A a_B & ( V_A V_B )^2= a_B 4 a_B & V_A V_B = 1 2 array ...[From (i)]