Question

2. A small electrically charged sphere is suspended vertically from a thread. An oppositely charged rod is
brought close to the sphere such that the sphere is in equilibrium displaced from the vertical by an angle of
30°. Which one of the following best represents the free body diagram for the SPHERE ?​

Answer 1

Free body diagram for the sphere:

• First of all, since the sphere is hanging from the string , it will be experiencing gravitational force (weight) downwards. It will be represented by a downward line.

• When the object with negative charge is being placed close to the positively charged sphere, the sphere is experiencing an attractive force towards the negative charge. So, it will be represented by a a line directed rightwards.

• And since, the the strings attached to the sphere, it will also experience a tension force along the string.

Now, applying Lami's Law:

$\dfrac{W}{ \sin( {120}^{ \circ} ) } = \dfrac{T}{ \sin( {90}^{ \circ} ) } = \dfrac{f}{ \sin( {150}^{ \circ} ) }$

$\implies \dfrac{W}{ \cos( {30}^{ \circ}) } = T = \dfrac{f}{ \cos( {60}^{ \circ} ) }$

Since value of cosine < 1 , so W > T, Similarly, f >T.

Again,

$\implies \dfrac{W}{ \cos( {30}^{ \circ}) } = \dfrac{f}{ \cos( {60}^{ \circ} ) }$

$\implies W =f \tan( {60}^{ \circ} )$

$\implies W > f$

So, final order is :

W > f > T

• W has longest line
• T has smallest line

Hope It Helps.