A cube bar slides thrice the time with friction than that without friction when it slides on an inclined plane of inclination 45^ . The coefficient of friction between the block and the surface is

Step-by-step solution

For a block sliding down an inclined plane of angle without friction, the acceleration is a₁ = g . The time taken to cover a distance s is t₁ = 2s a₁ = 2s g . For a block sliding down with friction, the acceleration is a₂ = g( - ) . The time taken to cover the same distance s is t₂ = 2s a₂ = 2s g( - ) . Given t₂ = 3t₁ , we have 2s g( - ) = 3 2s g . Squaring both sides, 1 - = 9 . Rearranging gives 9( - ) = , which simplifies to 8 = 9 . Thus, = 8 9 . Given = 45^ , 45^ = 1 , so = 8 9 0.888 . Answer: 0.88