Question

is the maximum force $F$ that can be applied on block $m _1$, so that both $m _1 \& m _2$ will move together? There is no friction between $m _1$ and the horizontal table. The coefficientof friction between ' $m _1$ ' and ' $m _2$ ' is $\mu$.

• A. $\mu m _2 g$
• B. $\mu\left(m_1+m_2\right) g$
• C. $\mu \frac{ m _1 m _2}{\left( m _1+ m _2\right)} g$
• D. $\mu m _1 g$

Answer 1

Answer: (B)

Given, force $F$ is the applied force on mass $m_1$.

As we know that,
$F=m a$
$a=\frac{F}{m}$
where, $a$ is acceleration of system.
$m=m_1+m_2 \text { i.e. mass of system } $
$\therefore a=\frac{F}{m_1+m_2}$
and since, there should be no relative motion between $m_1$ and $m_2$
$\therefore f=\mu N_2=m_2 a$
where, $f=$ friction force
and $N_2=$ normal reaction of mass $m_2$.
$ \therefore \mu m_2 g=m_2 \frac{F}{m_1+m_2} $
$\Rightarrow F=\mu\left(m_1+m_2\right) g$