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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. Which of the following statements is correct?


A
The contact force between block and the inclined plane is parallel to the incline.
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B
The contact force between block and the inclined plane is of magnitude m(g+a)
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C
The contact force between block and the inclined plane is perpendicular to the incline
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D
The contact force between block and the inclined plane is of magnitude mgcosθ
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Solution

The correct option is B 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)cosθ
f=m(g+a)sinθ

Contact force,
R=N2+f2
R=[m(g+a)cosθ]2+[m(g+a)sinθ]2=m(g+a)

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