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Two small spheres of masses M(1)andM(2) ...

Two small spheres of masses `M_(1)andM_(2)` are suspended by weightless insulating threads of lengths `L_(1)and L_(2)` The spheres carry charges `Q_(1)andq_(2)` respectively . The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of `theta_(1) and theta_(2)` as shown . Which one o fthe following conditions , if `theta_(1)= theta_(2)` ?

A

`M_(1) != M_(2),theta_(1)=theta_(2)`

B

`M_(1)=M_(2)`

C

`theta_(1)=theta_(2)`

D

`L_(1)=L_(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
For sphere 1 , in equilibrium

`T_(1) cos theta_(1) = M_(1)g`
and `T_(1) cos theta_(1) = F_(1)`
` :. " " ta theta_(1) = (F_(1))/(M_(1)g)`
Similarly for sphere 2 , `tan theta_(2) = (F_(2))/(M_(2)g)`
F is same on both the charges , `theta ` will be same only if their masses M are equal .
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Knowledge Check

  • Two small spheres of masses M_(1) and M_(2) are suspended by weightless insulating threads of lengths L_(1) and L_(2) The spheres carry charges Q_(1) and Q_(2) respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of theta_(1) and theta_(2) as shown. Which one of the following conditions is essential, if theta_(1)=theta_(2) ?

    A
    `M_(1)!=M_(2)" but "Q_(1)=Q_(2)`
    B
    `M_(1)=M_(2)`
    C
    `Q_(1)=Q_(2)`
    D
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  • Two small spheres of masses M_(1) and M_(2) are suspended to weightless insulating threads of lenghts L_(1) and L_(2) . The sphere carry charges Q_(1) and Q_(2) respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of theta _(1) ans theta_(2) as shown. When one of following conditions is essential, if theta_(1) = theta_(2)

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