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Question

A block of mass 1 kg is at rest relative to a smooth wedge moving leftwards with constant acceleration a=5 m/ s2. Let N be the normal reaction between the block and the wedge. Then
(g=10 m/s2)

  1. N=55 N
  2. N=15 N
  3. tanθ=12
  4. tanθ=2


Solution

The correct options are
A N=55 N
C tanθ=12
Given block of mass 1 kg at rest on the smooth inclined plane.
Wedge has an acceleration of 5 m/s2 so a pseudo-force of 5 N will act on block
And it’s direction will be Negative to the direction of wedge.
So, the block has these three forces acting on it
mg=10 N (downward), Normal (at an angle θ from vertical) and 5 N rightward
The normal force will be the resultant of mg and pseudo-force
=102+52
=125=55
We have tanθ=mamg
=510=12
Nsinθ=ma
Ncosθ=mg
N=ma2+g2 and tanθ=ag

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