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Standard XII

Physics

Periodic Motion

A small spher...

Question

A small sphere of mass $m$ and electric charge $q$ , is suspended by a light thread. A second sphere carrying a charge $q_{2}$ is placed directly below the first sphere at a distance $^{'} d^{'}$ away. Then :

tension in thread may reduce to zero if the spheres are positively charged

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tension in thread may reduce to zero if the spheres are oppositely charged

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tension in thread can never be zero

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tension in thread is independent of the nature of the charges

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Solution

The correct option is C tension in thread may reduce to zero if the spheres are positively charged
Tension in the string is balancing force to keep the sphere in equilibrium after being exerted by forces due to gravitation and Coulomb effect.
If the spheres are both positively charged, the small sphere experiences a force in the upward direction.
$⟹ T = m g - \frac{1}{4 π ϵ_{0}} \frac{q q_{2}}{d^{2}}$
For some particular distance $d$ , $T$ can be zero.
Hence correct answer is option A.

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A small sphere of mass m and electric charge q, is suspended by a light thread. A second sphere carrying a charge q2 is placed directly below the first sphere at a distance ′d′ away. Then :

A small sphere of mass $m$ and electric charge $q$ , is suspended by a light thread. A second sphere carrying a charge $q_{2}$ is placed directly below the first sphere at a distance $^{'} d^{'}$ away. Then :