Question

A block rests on a fixed rough inclined plane and a horizontal force $F$ is applied to it, as shown in the figure. Which of the following statements are correct?

(1) Normal reaction on the block is $Fsin \theta +mgcos ⁡ \theta $

(2) The frictional force is zero when $Fcos \theta =mgsin ⁡ \theta $

(3) The value of limiting friction is $\mu \left(\right.mgsin \theta +Fcos ⁡ \theta \left.\right)$

(4) The value of limiting friction is $\mu \left(\right.mgsin \theta -Fcos ⁡ \theta \left.\right)$

• A. 1, 2
• B. 3, 4
• C. 2, 4
• D. 2, 3

Answer 1

Answer: (A)

As the object is at rest, therefore from FBD,
Normal Reaction $N=mgcos \theta +Fsin ⁡ \theta $ .....(i)
Limiting Friction $f_{L}=\mu N=\mu \left(m g cos \theta + F sin ⁡ \theta \right)$ ......(ii) $ \, $
Also, if $mgsin \theta =Fcos ⁡ \theta $
then the object has no tendency of motion; hence friction is zero in this case.