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A body of mass 6kg rests on an inclined plane…

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A body of mass 6kg rests on an inclined plane...

A body of mass 6kg rests on an inclined plane. The normal reaction R and the limiting frictional force is F as shown in the diagram (Fig. 2). If F is 30N and g=10ms-2 , then the angle of inclination Ө is

A. 15°

B. 60°

C. 45°

D. 30°




For an object on an inclined plane, the resolution of the weight W along the plane, opposite the frictional force (F) is = Wsinө

While the resolution of the weight perpendicular to the plane and opposite the normal reaction (R) is = Wcosө

But we are given the value of F and not R, this is why we will use:

F = Wsinө

But weight W = mass (m) x acceleration due to gravity (g),

Therefore, F = mg sinө

Sin ө = F/mg

= 30/(6 × 10)

= 30/60

= 1/2

= 0.5

Therefore, ө = sin¯¹0.5 = 30°

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is incorrect.
  3. C is incorrect.
  4. D is the correct answer.


You may please note these/this:

  • Resolution of the weight of an object along the slope of the inclined plane is given by F = mg Sinө
  • Resolution of the same weight at 90 degrees to the plane is given by R = mg Cosө.
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/ culled from 2015 JAMB-UTME physics past question 4 /

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