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

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A. 15°

B. 60°

C. 45°

D. 30°

D

## DETAILS…

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.

## KEY-POINTS…

• 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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