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)` ?

Options

A. `M_(1) != M_(2),theta_(1)=theta_(2)`
B. `M_(1)=M_(2)`
C. `theta_(1)=theta_(2)`
D. `L_(1)=L_(2)`

Answer

B

Explanation

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 .