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

### System of Masses $m_1 + m_2 + m_3$

Three masses $m_1 , m_2 , m_3$ kept on a smooth horizontal surface under the influence of force F have got certain acceleration (refer figure). Find the force that mass $m_1$ exerts on mass $m_2$.

Solution

Let a be the acceleration.

Taking $m_1 + m_2 + m_3$ as system,

$F = (m_1 + m_2 + m_3)a$

$\Rightarrow a = \frac {F}{m_1 + m_2 + m_3 }$

Let N be the force that $m_1$ exerts on $m_2$. Taking $m_2 + m_3$ as system,

$N = (m_2 + m_3 ) a$

$\Rightarrow N = F. \frac {m_2 + m_3 }{m_1 + m_2 + m_3 }$

Interestingly, as $m_1 \to 0$, $N \to F$

### 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 = ${}^{12}{C_6} = 924$