A galvanometer of resistance 50 Ω gives a full scale deflection for a current 5 x 10^-4 A. The resistance that should be connected in series with the galvanometer to read 3 V is

• 5059 Ω

• 595 Ω

• 5950 Ω

• 5050 Ω

A cyclotron is used to accelerate

• only negatively charged particles

• neutron

• both positively and negatively charged particles

• only positively charged particles

A proton is projected with a uniform velocity v along the axis of a current-carrying solenoid, then

• the proton will be accelerated along the axis

• the proton path will be circular about the axis

• the proton move along helical path

• the proton will continue to move with velocity v along the axis

In the cyclotron, as radius of the circular path of the charged particle increases (ω = angular velocity, v = linear velocity)

• both ω and v increase

• ω only increases, v remains constant

• v increases, ω remains constant

• v increases, ω decreases

A conducting wire carrying current is  arranged as shown in the figure. The magnetic field at O is

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{12} \left[\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right]$

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{12} \left[\frac{1}{{\mathrm{R}}_1} + \frac{1}{{\mathrm{R}}_2}\right]$

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{6} \left[\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right]$

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{6} \left[\frac{1}{{\mathrm{R}}_1} + \frac{1}{{\mathrm{R}}_2}\right]$

A galvanometer coil has a resistance of 50 Ω and the meter shows full scale deflection for a current of 5 mA. This galvanometer is converted into voltmeter of range 0-20 V by connecting

• 3950 Ω in series with galvanometer

• 4050 Ω in series with galvanometer

• 3950 Ω in parallel with galvanometer

• 4050 Ω in parallel with galvanometer

A long solenoid with 40 turns per cm carries a current of 1 A. The magnetic energy stored per unit volume is

• $3.2 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

• $32 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

• $1.6 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

• $6.4 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

A proton, a deuteron and an α-particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths described by them is

• $1 : \sqrt{2} : 1$

• $1 : \sqrt{2} : \sqrt{2}$

• $\sqrt{2} : \sqrt{2} : 1$

• $\sqrt{2} : 1 : 1$

A galvanometer of resistance 50 Ω is connected to a battery of 3 V along with. a resistance of 2950 Ω in series shows full-scale deflection of 30 divisions. The additional series resistance required to reduce the deflection to 20 divisions is

• 2950 Ω

• 1500 Ω

• 4450 Ω

• 7400 Ω

A magnetic dipole of magnetic moment 6 × 10^-2 A-m² and moment of inertia 12 x 10^-6 kg-m² performs oscillations in a magnetic field of 2 x 10^-2 T. The time taken by the dipole to complete 20 oscillations is (π ≈ 3)

• 18 s

• 6 s

• 36 s

• 12 s