KVPY Sample Paper KVPY Stream-SX Model Paper-3

Two particles having the same specific charge (q/m) enter a uniform magnetic field with the same speed but an angles of \[30{}^\circ \] and \[60{}^\circ \] with the field. Let a, b and c be ratios of their pitches, radii and periods of their paths respectively, then:

A) \[a+b=2\sqrt{c}\]

B) \[abc=1\]

C) \[{{a}^{2}}=c\]

D) \[a{{b}^{2}}=c\]

Correct Answer: B

Solution :

\[T=\frac{2\pi m}{qB},\] \[p=\frac{2\pi m}{qB}v\cos \theta ,\] \[R=\frac{mv\sin \theta }{qB}\]

\[a=\frac{\cos {{\theta }_{1}}}{\cos {{\theta }_{2}}},\] \[b=\frac{sin{{\theta }_{1}}}{sin{{\theta }_{2}}},\] \[c=1\]

\[a=\sqrt{3},\] \[b=\frac{1}{\sqrt{3}},\] \[c=1.\]