In Q.48 , the block can be made to slide on the floor only if `theta` is more than a minimum value . Otherwise , the block cannot be made to slide by any value of F however large . Minimum value of `theta` for less than which sliding cannot happen , is :

Options

A. `sin^(-1) ((mu)/(sqrt(1 + mu^(2))))`
B. `cos^(-1) ((mu)/(sqrt(1 + mu^(2))))`
C. `tan^(-1) ((mu)/(sqrt(1 + mu^(2))))`
D. zero

Answer

A

Explanation

See Q.48. For motion , F must be positive .
`therefore` sin `theta - mu "cos " theta gt 0`
sin `theta gt mu cos theta `
`tan theta gt mu `
From the figure ,
`sin theta gt (mu)/(sqrt(1 + mu^(2)))`
`theta gt sin^(-1) ((mu)/(sqrt(1 + mu^(2))))`