Question

Three blocks are placed at rest on a smooth inclined plane with force acting on $m_{1}$ parallel to the inclined plane. Find the contact force between $m_{2}$ and $m_{3}$.

• A. $\frac{\left(m_{1}+m_{2}+m_{3}\right) F}{m}$
• B. $\frac{m_{3} F}{m+m+m}$
• C. $F-\left(m_{1}+m_{2}\right) g$
• D. None of these

Answer 1

Answer: (B)

Acceleration of system $a=\frac{\text { Net pushing force }}{\text { Total mass }}$
or $a=\frac{F-\left(m_{1}+m_{2}+m_{3}\right) g \sin \theta}{\left(m_{1}+m_{2}+m_{3}\right)}$
Equation of motion for $m_{3}$
$N-m_{3} g \,\sin \theta=m_{3} a$
or $N=m_{3} g \,\sin \theta+m_{3}\left\{\frac{F-\left(m_{1}+m_{2}+m_{3}\right) g \sin \theta}{\left(m_{1}+m_{2}+m_{3}\right)}\right\}$
$=\frac{m_{3} F}{m_{1}+m_{2}+m_{3}}$