A simple pendulum with a bob of mass 40 ~g and charge +2 C makes 20 oscillation in 44 ~s . A vertical electric field magnitude 4.2 10^4 NC ⁻¹ pointing downward is applied. The time taken by the pendulum to make 15 oscillation in the electric field is (acceleration due to gravity =10 ~ms ⁻² )

Step-by-step solution

Mass, m=40 ~g =0.04 ~kg , q=2 10⁻⁶ C Now, m a=q E aligned a & = q m E & = 2 10⁻⁶ 0.04 4.2 10^4 ~m / s ^2 & =2.1 ~m / s ^2( downward ) aligned So, effective acceleration on bob, a_e=a+g=12.1 ~m / s ^2 In the absence of electric field, T=2 l g =2 l 10 In the presence of electric field, aligned T^ & =2 l a_e =2 l 12.1 T T^ & = 12.1 10 = 11 10 T^ = 10 11 T aligned Given, T= 44 20 T^ = 10 11 44 20 =2 ~s So, time taken in 15 oscillations =2 15=30 ~s