Question

A block of mass $m$ is at rest with respect to a rough inclined plane kept in an elevator moving up with an acceleration $‘a^{\prime }$. Which of the following statements is correct?

• A. $\text{The contact force between block and the inclined plane is parallel to the incline.}$
• B. $\text{The contact force between block and the inclined plane is of magnitude}m(g+a)$
• C. $\text{The contact force between block and the inclined plane is perpendicular to the incline}$
• D. $\text{The contact force between block and the inclined plane is of magnitude}mg\cos \theta$

Answer 1

The correct option is B $\text{The contact force between block and the inclined plane is of magnitude}m(g+a)$

The FBD of the block is as shown in the reference frame of elevator which is going up with an acceleration of $a$


From the FBD, using concept of pseudo force we have at equilibrium
$N=m(g+a)\cos \theta$
$f=m(g+a)\sin \theta$

$\therefore$ Contact force,
$R=\sqrt{N^2+f^2}$
$\Rightarrow R=\sqrt{\left[m\right(g+a)\cos \theta {]}^2+[m(g+a)\sin \theta {]}^2}=m(g+a)$