In the diagram shown, the charge +Q is fixed. Another charge +2 q, is projected from a distance R from the fixed charge. The minimum separation between the two charges when the velocity becomes (1/√3) times of the projected velocity, is (Assume gravity to be absent)

Question

In the diagram shown, the charge +Q is fixed. Another charge +2 q, is projected from a distance R from the fixed charge. The minimum separation between the two charges when the velocity becomes (1/√3) times of the projected velocity, is (Assume gravity to be absent) (A) (√3/2) R (B) √3 R (C) (1/2) R (D) 4 R

Tardigrade Admin · Accepted Answer

Using conservation of angular momentum about fixed charged, M V sin 30° × R=M v prime × r ⇒ (V/2) R=(V/√3) r r=(√3/2) R

Q. In the diagram shown, the charge $+ Q$ is fixed. Another charge $+ 2 q$ , is projected from a distance $R$ from the fixed charge. The minimum separation between the two charges when the velocity becomes $\frac{1}{3}$ times of the projected velocity, is (Assume gravity to be absent)

$\frac{3}{2} R$

$3 R$

$\frac{1}{2} R$

$4 R$

Using conservation of angular momentum about fixed charged,
$M V sin 3 0^{\circ} \times R = M v^{'} \times r$
$\Rightarrow \frac{V}{2} R = \frac{V}{3} r$
$r = \frac{3}{2} R$

Q. In the diagram shown, the charge +Q is fixed. Another charge +2q, is projected from a distance R from the fixed charge. The minimum separation between the two charges when the velocity becomes 3​1​ times of the projected velocity, is (Assume gravity to be absent)

23​​R

3​R

21​R

4R