Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6: 5 and their respective masses ratio is 9: 4. Then, the ratio of their charges will be :

Question

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6: 5 and their respective masses ratio is 9: 4. Then, the ratio of their charges will be : (A) 8: 5 (B) 5: 4 (C) 5: 3 (D) 8: 7

Tardigrade Admin · Accepted Answer

Radius of circular path R =(√2 mk / qB ) q =(√2 mk / RB ) ( q 1/ q 2)=√( m 1/ m 2) × ( R 2/ R 1)=√(9/4) × (5/6)=(5/4)

Q. Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $6 : 5$ and their respective masses ratio is $9 : 4$ . Then, the ratio of their charges will be :

$8 : 5$

$5 : 4$

$5 : 3$

$8 : 7$

Radius of circular path $R = \frac{2 mk}{qB}$
$q = \frac{2 mk}{RB}$
$\frac{q _{1}}{q _{2}} = \frac{m _{1}}{m _{2}} \times \frac{R _{2}}{R _{1}} = \frac{9}{4} \times \frac{5}{6} = \frac{5}{4}$

Q. Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6:5 and their respective masses ratio is 9:4. Then, the ratio of their charges will be :

8:5

5:4

5:3

8:7