Two identical small beads each have mass m and charge q. When placed on a fixed hemispherical bowl of radius R with frictionless nonconducting walls, the beads move, and at equilibrium they are distance R from each other. Determine the charge on each bead (in μ C ). Take m=9 √3 mg , R =10 m.

Question

Two identical small beads each have mass m and charge q. When placed on a fixed hemispherical bowl of radius R with frictionless nonconducting walls, the beads move, and at equilibrium they are distance R from each other. Determine the charge on each bead (in μ C ). Take m=9 √3 mg , R =10 m. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/d315998f4a89da495e1ce44e265673a1-.png" /> mg cos 60°=( kq 2/ R 2) cos 30° q =√( mgR 2/ k × √3)=√(2 √3 × 10-6 × 10 × 102/9 × 109 × √3) =10-6 C =1 μ C

Q. Two identical small beads each have mass m and charge q. When placed on a fixed hemispherical bowl of radius R with frictionless nonconducting walls, the beads move, and at equilibrium they are distance R from each other. Determine the charge on each bead (in μC ). Take m=93​mg,R=10m.

mgcos60∘=R2kq2​cos30∘ q=k×3​mgR2​​=9×109×3​23​×10−6×10×102​​ =10−6C=1μC

$m g cos 6 0^{\circ} = \frac{k q ^{2}}{R ^{2}} cos 3 0^{\circ}$
$q = \frac{m g R ^{2}}{k \times 3} = \frac{2 3 \times 1 0 ^{- 6} \times 10 \times 1 0 ^{2}}{9 \times 1 0 ^{9} \times 3}$
$= 1 0^{- 6} C = 1 μ C$