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Q.

A particle having mass m, charge q is projected with velocity v0 along y- axis in a region of uniform magnetic field B0  which is outward and perpendicular to the plane of the paper as shown in the figure. The particle is continuously subjected to a frictional force which varies with velocity as Fr=αV, where α is a constant. Consequently the particle moves on a spiral path till it comes to rest at point P. The x-co-ordinate of point P is 5K. Find K? 
(Take α=103kg/s; q=103C; B0=1T, v0=1m/s, m=20gm)
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Detailed Solution

ω=qBm            θ=qBmt           v=v0eαtm             vx=v0eαtmsinqBmt                 vx=v0et20sint20          x=v00et20sint20x=10

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A particle having mass m, charge q is projected with velocity v0 along y- axis in a region of uniform magnetic field B0  which is outward and perpendicular to the plane of the paper as shown in the figure. The particle is continuously subjected to a frictional force which varies with velocity as F→r=−αV→, where α is a constant. Consequently the particle moves on a spiral path till it comes to rest at point P. The x-co-ordinate of point P is 5K. Find K? (Take α=10−3kg/s; q=10−3C; B0=1T, v0=1m/s, m=20gm)