Three concentric metallic spherical shells of radii $R, 2 R, 3 R$ are given charges $Q_{1}, Q_{2}, Q_{3}$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells $Q_{1} : Q_{2} : Q_{3}$ is

1 : 4 : 9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 2 : 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 3 : 5

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 : 8 : 18

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $1 : 3 : 5$

$σ = \frac{Q_{1}}{4 π R^{2}} σ = \frac{Q_{1} + Q_{2}}{16 π R^{2}} σ = \frac{Q_{1} + Q_{2} + Q_{3}}{36 π R^{2}}$

$1 = \frac{4 Q_{1}}{Q_{2} + Q_{1}} \Rightarrow \frac{Q_{2} + Q_{1}}{4 Q_{1}} = 1$

$\frac{Q_{2}}{Q_{1}} = 3$ ---- (1)

Also,

$1 = \frac{9 (Q_{2} + Q_{1})}{4 (Q_{3} + Q_{2} + Q_{1})}$

From eq. $(1), Q_{2} = 3 Q_{1}$

$\Rightarrow \frac{Q_{3}}{Q_{1}} = 5$ ---- (2)

From (1) & (2)
$Q_{1} : Q_{2} : Q_{3} = 1 : 3 : 5$

Suggest Corrections

Similar questions

R, 2 R, 3 R

Q_{1}, Q_{2}, Q_{3}

Q_{1} : Q_{2} : Q_{3}

q_{1}

q_{2}

q_{3}

Join BYJU'S Learning Program