The bob of a simple pendulum as a mass of 40g and a positive charge of 4.0 × 10–6 C. It makes 20 oscillations in 45s. A vertical electric field pointing upward and the magnitude 2.5 × 104 N C–1 is switched on. How much time will it now take to complete 20 oscillations?
Mass of the bob: m = 40 g = 0.04 kg
Charge of the bob: q = 4.0 × 10–6 C
Oscillations in t=45s : 20
Vertical electric field: E = 2.5 × 104 N C–1.
Formula used:
Time period of a simple pendulum is:
here l is the length of the string .
Thus, when there is no electric field, the time period is:
When a vertical electric field is applied, the positively charged bob will experience a vertical acceleration due to electric force. Thus net acceleration of the bob = g-a
Time period of the simple pendulum when vertical electric field applied is:
Now,
Since a is due to electric force, by Newton’s Second Law and Formula for electric force, we get
Thus g-a = 9.8-2.5 = 7.3 m/s2
Taking ratio we get:
Hence time required by the bob to complete 20 oscillations in presence of a vertical electric field is 52 seconds.