a proton a deuteron and an alpha particle having the same

A proton, a deuteron and an $$\alpha - $$ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $${r_p},{r_d},$$ and $${r_\alpha }$$ denote respectively the radii of the trajectories of these particles, then

A. $${r_\alpha } = {r_p} < {r_d}$$

B. $${r_\alpha } > {r_d} > {r_p}$$

C. $${r_\alpha } = {r_d} > {r_p}$$

D. $${r_p} = {r_d} = {r_\alpha }$$

Answer : $${r_\alpha } = {r_p} < {r_d}$$

Solution :
KEY CONCEPT: $$r \propto \frac{{\sqrt m }}{q}$$
$$\eqalign{ & \therefore {r_p}:{r_d}:{r_\alpha } = \frac{{\sqrt 1 }}{1}:\frac{{\sqrt 2 }}{1}:\frac{{\sqrt 4 }}{1} = 1:\sqrt 2 :1 \cr & \Rightarrow {r_\alpha } = {r_p} < {r_d} \cr} $$

Releted MCQ Question on
Electrostatics and Magnetism >> Magnetic Effect of Current

Releted Question 1

A conducting circular loop of radius $$r$$ carries a constant current $$i.$$ It is placed in a uniform magnetic field $${{\vec B}_0}$$ such that $${{\vec B}_0}$$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is

A. $$ir\,{B_0}$$

B. $$2\pi \,ir\,{B_0}$$

C. zero

D. $$\pi \,ir\,{B_0}$$

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Releted Question 2

A battery is connected between two points $$A$$ and $$B$$ on the circumference of a uniform conducting ring of radius $$r$$ and resistance $$R.$$ One of the arcs $$AB$$ of the ring subtends an angle $$\theta $$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

A. proportional to $$2\left( {{{180}^ \circ } - \theta } \right)$$

B. inversely proportional to $$r$$

C. zero, only if $$\theta = {180^ \circ }$$

D. zero for all values of $$\theta $$

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Releted Question 3