The concentric, conducting spherical shells X, Y and Z with radii r, 2r and 3r, respectively. X and Z are connected by a conducting wire and Y is uniformly charged to charge Q as shown in figure. Charges on shells X and Z will be

• ${\mathrm{q}}_{\mathrm{x}} = \frac{-\mathrm{Q}}{4}, {\mathrm{q}}_{\mathrm{z}} = \frac{\mathrm{Q}}{4}$

• ${\mathrm{q}}_{\mathrm{x}} = \frac{\mathrm{Q}}{4}, {\mathrm{q}}_{\mathrm{z}} = \frac{-\mathrm{Q}}{4}$

• ${\mathrm{q}}_{\mathrm{x}} = \frac{\mathrm{Q}}{4} , {\mathrm{q}}_{\mathrm{z}} = \frac{\mathrm{Q}}{4}$

• ${\mathrm{q}}_{\mathrm{x}} = \frac{-\mathrm{Q}}{6}, {\mathrm{q}}_{\mathrm{z}} = \frac{\mathrm{Q}}{4}$

In the given figure, the capacitors C₁, C₃, C₄, C₅ have a capacitance 4 µF each. If the capacitor C₂ has a capacitance 10 μF, then effective capacitance between A and B will be 

• 2 μF

• 6 μF

• 4 μF

• 8 μF

A capacitor is charged and then made to discharge through a resistance. The time constant is t. In what time will the potential difference across the capacitor decrease by 10 %?

• τ ln 0.1

• τ ln 0.9

• τ ln$\frac{10}{9}$

• τ ln$\frac{11}{10}$

As shown in figure, two vertical conducting rails separated by distance 1.0 m are placed parallel to z-axis. At z = 0, a capacitor of 0.15 F is connected between the rails and a metal rod of mass 100 gm placed across the rails slides down along the rails. If a constant magnetic fields of 2.0 T exists perpendicular to the plane of the rails, what is the acceleration of the rod? ( take g = 9.8 m/s²)

• 2.5 m/s²

• 1.4 m/s²

• 9.8 m/s²

• 0

A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel through its centre. A small particle with negative charge, initially at rest far from the sphere, approaches it along the line of the tunnel, reaches its surface with a speed v, and passes through the tunnel. Its speed at the centre of the sphere will be

• 0

• v

• $\sqrt{2}$v

• $\sqrt{1.5}$ v

In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is however not constant, but increases uniformly along the positive z-direction at the rate of 10⁵ N C^-1m^-1 The force experienced by the system having a total dipole moment equal to 10^-7 C m in the negative z-direction is

• $-$10^-2 N

• 10^-2 N

• 10^-4 N

• $-$ 10^-4 N

An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negative charge upto a radius R. The atom as a whole is neutral. The electric field at a distance r from the nucleus is (r < R)

• $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0} \left[\frac{1}{{\mathrm{r}}^2} - \frac{\mathrm{r}}{{\mathrm{R}}^3}\right]$

• $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0} \left[\frac{1}{{\mathrm{r}}^3} - \frac{\mathrm{r}}{{\mathrm{R}}^2}\right]$

• $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0} \left[\frac{\mathrm{r}}{{\mathrm{R}}^3} - \frac{1}{{\mathrm{r}}^2}\right]$

• $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0} \left[\frac{\mathrm{r}}{{\mathrm{R}}^3} + \frac{1}{{\mathrm{r}}^2}\right]$

A deflection magnetometer is adjusted in the usual way. When a magnet is introduced, the deflection observed is θ, and the period of oscillation of the needle in the magnetometer is T. When the magnet is removed, the period of oscillation is T₀. The relation between T and T₀ is

• T² = ${\mathrm{T}}_0^2$ cosθ

• T = T₀ cosθ

• T = $\frac{{\mathrm{T}}_0}{\cos \mathrm{\theta }}$

• ${\mathrm{T}}^2 = \frac{{\mathrm{T}}_0^2}{\mathrm{cos\theta }}$

A parallel plate capacitor with air as a dielectric has capacitance C. A slab of dielectric constant K, having same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

• $\left(\mathrm{K} + 3\right) \frac{\mathrm{C}}{4}$

• $\left( \mathrm{K} + 2 \right) \frac{\mathrm{C}}{4}$

• $\left(\mathrm{K} + 1\right) \frac{\mathrm{C}}{4}$

• $\frac{\mathrm{K} \mathrm{C}}{4}$

Assertion:  If a dielectric is placed in external field then field inside dielectric will be less than applied field.

Reason:  Electric field will induce dipole moment opposite to field direction.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.