Visit the website 123iitjee.manishverma.site for latest posts, courses, admission & more.

### An $\alpha$-particle (mass 4 amu) and a singly ....

An $\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_{\alpha}$ and $r_S$, respectively. The ratio ($r_S/r_\alpha$) is _____.

Solution

$r = \sqrt {\frac{{2mV}}{{q{B^2}}}}$

So, $r \propto \sqrt {\frac{m}{q}}$

$\frac{{{r_S}}}{{{r_\alpha }}} = \sqrt {\frac{{{m_S}}}{{{q_S}}} \times \frac{{{q_\alpha }}}{{{m_\alpha }}}} = \sqrt {\frac{{{m_S}}}{{{m_\alpha }}} \times \frac{{{q_\alpha }}}{{{q_S}}}} = \sqrt {\frac{{32}}{4} \times \frac{2}{1}} = 4$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$