Minimum force is needed to move a block on rought surface, if `theta =` angle of friction.
Angle of friction and angle of repose are numerically same.

Options

A. If both Accertion and Reason are true and the reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Answer

B

Explanation

`N = m g- F sin theta`

`F cos theta = mu N = mu (mg - F sin theta)`
`:. F = (mu mg)/(cos theta + mu sin theta) = f (theta)` …(i)
For `F` to be minimum, denominator should be maximum.
or `(d)/(d theta) (cos theta + mu sin theta) = 0`
From here we get `theta = tan ^(-1) (mu) =`angle of friction. with this value of `theta` we can also find that minimum value of force required from Eq. (i).