A block takes t time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time t 2 to slide down the plane. The coefficient of friction between the block and the inclined plane is ( 100 ) . The value of is __________.

Step-by-step solution

Let the length of the inclined plane be s . For the smooth inclined plane, the acceleration of the block is a₁ = g . The time taken is t₁ = t 2 . Using the second equation of motion s = ut + 1 2 at^2 with u = 0 : s = 1 2 (g ) ( t 2 )^2 = 1 8 g t^2 For the rough inclined plane, the acceleration of the block is a₂ = g( - ) . The time taken is t₂ = t . Using the equation of motion again: s = 1 2 g( - ) t^2 Equating the two expressions for s : 1 8 g t^2 = 1 2 g( - ) t^2 1 4 = - Given = 45^ , we have 45^ = 45^ = 1 2 . S