A body of mass 1 ~g and carrying a charge 10⁻⁸ C passes from two points P and Q . P and Q are at electric potentials. 600 ~V and 0 ~V , respectively. The velocity of the body at Q is 20 cms ⁻¹ . It velocity in ms ⁻¹ at P is

Step-by-step solution

aligned m & =1 ~g =10⁻³ ~kg , v & =20 ~cm / s =20 10⁻²⁰ ~m / s q & =10⁻⁸ C V_p & =600 volt V_Q & =0 volt aligned Work done in moving the charge from P to Q aligned W & =q V_ P Q =10⁻⁸(600-0) & =600 10⁻⁸ ~J aligned From work energy theorem Work done = change in KE aligned 600 10⁻⁸ & = 1 2 m (20 10⁻² )^2- 1 2 m v^2 600 10⁻⁸ & = 1 2 10⁻³ 4 10⁻²- 1 2 10⁻³ v^2 1 2 10⁻³ v^2 & =2 10⁻⁵-600 10⁻⁸ & =2 10⁻⁵-0.6 10⁻⁵ v^2 & =1.4 10⁻² 2=28 10⁻² v & = 28 10⁻² = 0.028 ~m / s aligned