AP EAMCET202021 Sep 2020Morning ShiftPhysicsElectrostaticsActual
A charged cork ball having mass (1 g ) and charge (q ) is suspended on a light string in a uniform electric field as shown in figure. The ball is in equilibrium at ( =37^ ), when value of electric field is ( E =(3 i +5 j ) 10^5 NC ⁻¹ ). (Assume, (T ) as tension in the string.) Which of the following options are correct? (Given, ( 37^ =0.60 ) and (g=10 ~ms ⁻² ) )
Options
- A(q=11 10⁻⁸ C )
- B(T=5.55 10⁻³ ~N )
- C(q=12 10⁻⁹ C )
- D(T=4.55 10⁻³ ~N )
Correct answer
B. (T=5.55 10⁻³ ~N )
Step-by-step solution
Mass of cork ball, (m=1 ~g =10⁻³ ~kg ) ( aligned & E =(3 i +5 j ) 10^5 NC ⁻¹ & =37^ aligned ) Force on cork ball due to electric field ( E ) ( F =q E ) According to given diagram, resolving all forces in two given direction, ( array ll & T =q E_x (i) & T +q E_y=m g & T =m g-q E_y (ii) array ) From Eqs. (i) and (ii), we have ( T T = q E_x m g-q E_y ) ( aligned & = q E_x m g-q E_y & 37^ = q 3 10^5 10⁻³ 10-q 5 10^5 & 3 4 = 3 q 10^5 10⁻²-5 q 10^5 & 3 10⁻²-15 q 10^5=4 3 q 10^5 & 0.03-15 10^5 q=12 10^5 q q=11 10⁻⁸ C alig