Question

A sphere A of mass $2$kg is in contact with a rectangular block B of mass $4$kg and vertical wall as shown in the figure. All surfaces are smooth. If normal reaction by the vertical wall on the sphere A is $9$X Newtons, then find the value of X. $(g=10m/s^2)$.

Answer 1

Balancing forces

$M_{A}gcos37+N_{wall}cos53=N_A$

$N_{AB}+M_{A}gsin37=N_{wall}sin53$

$N_{AB}=Mgsin37$

$N_B=Mgcos37$

$M_A=2$

$M_B=4$

$N_{AB}=4g\ast \frac{5}{3}=\frac{12g}{5}$

$\frac{12g}{5}+2g\ast \frac{3}{5}=N_{wall}\frac{4}{5}$

$\frac{18g}{5}=N_{wall}\ast \frac{4}{5}$

$N_{wall}=\frac{9g}{2}$

$x=\frac{g}{2}=5m/s^2$