A block of mass `1 kg` is placed on a rough inclined plane at angle ` theta = 45^(@)` will horizontal . The block is connected with a straight as straight as shown in figure if `mu = 3//4` find the tension in string

Explanation

Let us first find the angle of repose i.e., the angle of inclination of inclined plane with horizontal sach that when body placed on it just begning to slide down As we know the angle of repose
`a = tan^(-1) (mu_(s)) = tan^(-1)((3)/(4)) = 37^(@)`

Here the angle of inclination of plase is less then the angle of repose. Here the block does not have tendency to side The friction force between the block and incline is static nature
`f = mg sin theta = 1 xx 10 xx sin 30^(@) = 5 N`
Hence tension in string is string will be zero