1
JEE Advanced 2021 Paper 1 Online
Numerical
+4
-0
An $$\alpha$$-particle (mass 4 amu) and a singly charged sulphur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $$\alpha$$-particle and the sulfur ion move in circular orbits of radii r$$\alpha$$ and rs, respectively. The ratio (rs/r$$\alpha$$) is __________.
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2
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
A moving coil galvanometer has $$50$$ turns and each turn has an area $$2 \times {10^{ - 4}}\,{m^2}.$$ The magnetic field produced by the magnet inside the galvanometer is $$0.02$$ $$T.$$ The torsional constant of the suspension wire is $${10^{ - 4}}\,N\,m\,ra{d^{ - 1}}.$$ When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by $$0.2$$ $$rad$$. The resistance of the coil of the galvanometer is $$50\Omega .$$ This galvanometer is to be converted into an ammeter capable of measuring current in the range $$0-1.0$$ $$A$$. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is _____________.
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3
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
In the $$xy$$-plane, the region $$y > 0$$ has a uniform magnetic field $${B_1}\widehat k$$ and the region $$y < 0$$ has another uniform magnetic field $${B_2}\widehat k.$$ A positively charged particle is projected from the origin along the positive $$y$$-axis with speed $${v_0} = \pi \,m{s^{ - 1}}$$ at $$t=0,$$ as shown in the figure. Neglect gravity in this problem. Let $$t=T$$ be the time when the particle crosses the $$x$$-axis from below for the first time. If $${B_2} = 4{B_1},$$ the average speed of the particle, in $$m{s^{ - 1}},$$ along the $$x$$-axis in the time interval $$T$$ is ___________.

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4
JEE Advanced 2014 Paper 1 Offline
Numerical
+3
-0
Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R2. If $${{{X_0}} \over {{X_1}}} = 3$$, and value of R1/R2 is
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