Question

Answer the question ensure it’s correct

Answer 1

▶ Solution :

Given :

▪ A pendulum bob carries a charge -q.

▪ A positive charge +q is held at the point of support.

To Find :

▪ Time period of pendulum.

Concept :

▪ This question is completely based on concept of 'Electric field'.

▪ Direction of electric field due to positive charge is always away from it while due to negative charge always towards it.

▪ Formula of time period of simple pendulum is given by

$\underline{\boxed{\bf{\pink{T=2\pi\sqrt{\dfrac{l}{g}}}}}}$

• T denotes Time period
• l denotes length of pendulum
• g denotes net downward acceleration

✏ First, see the attachment for better understanding.

Calculation :

$\implies\bf\:F_{net}=F_{weight}+F_{electrical}\\ \\ \sf\:F_{net}=mg+qE\\ \\ \sf\:ma=mg+qE\\ \\ \bf\:\red{a_{eff}=g+\dfrac{qE}{m}}\\ \\ \implies\sf\:T=2\pi\sqrt{\dfrac{l}{a_{eff}}}\\ \\ \implies\sf\:T=2\pi\sqrt{\dfrac{l}{g+\frac{qE}{m}}}\\ \\ \implies\bf\:2\pi\sqrt{\dfrac{l}{g}}>2\pi\sqrt{\dfrac{l}{g+\frac{qE}{m}}}\\ \\ \implies\boxed{\bf{\purple{T<2\pi\sqrt{\dfrac{l}{g}}}}}$

✒ Option : B) is correct !