Statement-1: A proton and an `alpha`- particle are projected with the same kinetic energy at right angles to a uniform magnetic field, then the `alpha`-particle will move along a circular path of smaller radius than the proton.
Statement-2: `Bqv=(mv^2)/(r)`

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explaination of Statement-1.
B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation of Statement-1.
C. Statement-1 is true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true.

Answer

D

Explanation

`E=1/2mv^2` or `v=sqrt(2E//m)`
`Bqv=mv^2//r`
or `r=(mv)/(Bq)=(m)/(Bq)sqrt((2E)/(m))=(sqrt(2mE))/(Bq)`
i.e., `rpropsqrtm/q`
`:. r_p/r_alpha=sqrt((m_p)/(m_alpha))xxq_alpha/q_p=sqrt(1/4)xx2/1=1`
i.e., radius of both the particles should be the same. Hence statement-1 is wrong and statement-2 is correct.