Explanation:

Magnetic Force on a Charged Particle:
When a charged particle moves in a magnetic field, it experiences a force called the magnetic force. The magnitude of this force is given by the equation:

F = q*v*B*sin(θ)

where F is the magnetic force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.

Centripetal Force:
When a charged particle moves in a circular orbit, it experiences a centripetal force towards the center of the orbit. This force is given by the equation:

F = (mv^2)/r

where F is the centripetal force, m is the mass of the particle, v is the velocity of the particle, and r is the radius of the orbit.

Comparison between He and Li particles:
Since both He and Li particles are projected in a circular orbit of the same radius perpendicular to the magnetic field, the radius of the orbit (r) is the same for both particles.

Now, let's compare the velocities of the two particles:

- The magnetic force experienced by the particles is given by F = q*v*B*sin(θ).
- The magnitude of the magnetic force is the same for both particles since the charge (q) and magnetic field strength (B) are the same.
- The angle (θ) between the velocity vector and the magnetic field vector is 90 degrees for both particles since they are projected perpendicular to the magnetic field.
- Therefore, the magnitudes of the magnetic forces experienced by He and Li particles are the same.

Centripetal force:
- The centripetal force experienced by the particles is given by F = (mv^2)/r.
- Since the radius of the orbit (r) is the same for both particles, the magnitudes of the centripetal forces are the same for He and Li particles.
- Since the magnitude of the magnetic force is the same for both particles, the magnitudes of the velocities of the particles can be compared using the equation F = q*v*B*sin(θ).

Comparison of velocities:
- Since the magnitudes of the magnetic forces and centripetal forces are the same for both particles, we can equate the two equations:
(q*v*B*sin(θ)) = (mv^2)/r

Conclusion:
- Since the charge (q) and magnetic field strength (B) are the same for both particles, the equation becomes v = (m*q*r*B*sin(θ))/m.
- The mass (m) cancels out in the equation, and we are left with v = q*r*B*sin(θ).
- Since the radius of the orbit (r) and the angle (θ) are the same for both particles, the only difference is the charge (q).
- The charge of He is 2e, where e is the elementary charge, and the charge of Li is e.
- Since the charge of He is greater than the charge of Li, the velocity of He will be smaller than the velocity of Li.

Therefore, the correct answer is option 'A': the velocity will be smaller for He.