Three capacitors of capacitances 1 µF, 2µF and 4μF are connected first in a series combination and then in a parallel combination. The ratio their equivalent capacitances will be

• 2 : 49

• 49 : 2

• 4 : 49

• 49 : 4

A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the 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

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

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

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

• $\frac{\mathrm{KC}}{4}$

A parallel palte condenser is filled with two dielectrics as shown in figure. Area of each pate is A m² and the separation is d metre. The dielectric constants are K₁ and K₂ respectively. Its capacitance in farad will be

• $\frac{2 {\mathrm{\epsilon }}_{\mathrm{o}}\mathrm{A}}{\mathrm{d}}\left(\frac{{\mathrm{K}}_1 + {\mathrm{K}}_2}{{\mathrm{K}}_1 {\mathrm{K}}_2}\right)$

• $\frac{2{\mathrm{\epsilon }}_{\mathrm{o}} \mathrm{A}}{\mathrm{d}} \left(\frac{{\mathrm{K}}_1 {\mathrm{K}}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}\right)$

• $\frac{{\mathrm{\epsilon }}_{\mathrm{o}} \mathrm{A}}{\mathrm{d}} \left(\frac{{\mathrm{K}}_1 + {\mathrm{K}}_2}{2{\mathrm{K}}_1 {\mathrm{K}}_2}\right)$

• $\frac{{\mathrm{\epsilon }}_{\mathrm{o}} \mathrm{A} {\mathrm{K}}_1 {\mathrm{K}}_2}{2 \left({\mathrm{d}}_2 {\mathrm{K}}_1 + {\mathrm{d}}_1{\mathrm{K}}_2 \right)}$

Two equal negative charges - q are fixed at the point (0, a) and (0, - a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge wil

• execute SHM about the origin

• move to the origin and remain at rest

• move to infinity

• execute oscillatory but not SHM

A charged particle is accelerated by a potential of 200 V. If its velocity is 8.4 × 10⁸ m/s, then value  of e/m for that particle is

• 17.6 × 10¹⁶

• 14.5 × 10¹²

• 1.76 × 10¹⁵

• 1.45 × 10¹⁵

Two capacitors of capacities C₁ and C₂ are charged upto the potential V₁ and V₂ then condition for not flowing the charge between on connected them in parallel is

• C₁ = C₂

• C₁V₁ = C₂V₂

• V₁ =V₂

• $\frac{{\mathrm{C}}_1}{{\mathrm{V}}_2} =\frac{{\mathrm{C}}_2}{{\mathrm{V}}_2}$

167.

If V =ary, then electric field at a point will be proportional to

• r

• r ^-1

• r ^-2

• r²

Electric field at point 20 cm away from the centre of dielectric sphere is 100 V/m, radius of sphere is 10 cm, then the value of electric field at a distance 3 cm from the centre is

• 100 V/m

• 125 V/m

• 120 V/m

• 0

Magnetic field of the earth is H =0.3 g. A magnet is vibrating 5 oscillations per min then the dippreciation required in the magnetic field of the earth of increase time period upto 10 oscillations per minute is

• 2.25 g

• 0.6 g

• 0.9 g

• 0.12 g

Two small balls, each carrying a charge q are suspended by equal insulator strings of length l m from the hook of a stand. This arrangement is carried in a satellite in space. The tension in each string will be

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{\mathrm{q}}{{\mathrm{l}}^2}$

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{{\mathrm{q}}^2}{4{\mathrm{l}}^2}$

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{{\mathrm{q}}^2}{{\mathrm{l}}^2}$

• $\frac{1}{\left(4{\mathrm{\pi \epsilon }}_0\right)} \frac{\mathrm{q}}{\mathrm{l}}$