Question

21. A charged cark ball of mass 2 kg is suspended by light insulated string in electric field (Ē ) as shown, find the charge on ball, if it is in equilibrium :- ]
(1) 20 (2) 5C (3) 10C (4) 20 C​

Answer 1

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Refer to the attachment

Explanation:

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Answer 2

Answer:

The charge is 10C.

The correct option is 3.

Explanation:

Given:

$E_{y}=1j$

$E_{x}=1i$

m = 2Kg

g = $10m/s^{2}$

$\theta=45$°

Here,

The electric field in the direction of the y-axis is denoted by $E_{y}$.

The electric field in the direction of the x-axis is denoted by $E_{x}$.

The charge is denoted by q.

The mass is denoted by m.

The acceleration due to gravity is denoted by g.

The angle between the string and the y-axis is denoted by $\theta$.

The tension is denoted by T.

Now,

Balance the forces that act on the ball,

$Tcos\theta+qE_{y}=mg\\Tcos45+q\times1=2\times10\\\frac{T}{\sqrt{2} } +q=20$       .........(1)

And

$Tsin\theta=qE_{x}\\Tsin45=q\times1\\\frac{T}{\sqrt{2} } =q$                      ........(2)

On solving the equations one and two,

$T =10\sqrt{2}N$

q = 10C

So, the charge is 10C.