Friction

0.3

Step 1: The formula for coefficient of kinetic friction is: μ_k = f_k / R. Step 2: Substitute the values: μ_k = 30 / 100. Step 3: μ_k = 0.3. Wrong options: 0.1 uses f_k/R with wrong calculation; 0.2 is a common guess error; 3.0 inverts the ratio (R/f_k instead of f_k/R). The coefficient of friction is a dimensionless number.

Rolling friction is much less than sliding friction

Step 1: When a body rolls, only a tiny portion of it is in contact with the surface at any instant. Step 2: This contact portion is momentarily at rest, so very little work is done against friction. Step 3: Therefore, rolling friction (f_r) << kinetic friction (f_k) << static friction (f_s). Step 4: This is why vehicles use wheels — to reduce friction. Step 5: Rolling friction also depends inversely on the radius of the wheel (f_r = μ_r × R/r), so the last option is also incorrect.

3.27 m/s²

Step 1: The formula for acceleration down a rough incline is: a = g(sin θ - μ_k cos θ). Step 2: Substitute values: a = 10 × (sin 30° - 0.2 × cos 30°). Step 3: a = 10 × (0.5 - 0.2 × 0.866). Step 4: a = 10 × (0.5 - 0.1732) = 10 × 0.3268 = 3.27 m/s². Wrong options: 5.0 m/s² ignores friction entirely (a = g sin θ only); 1.73 m/s² uses only the friction term; 4.13 m/s² results from adding instead of subtracting friction.

Strong atomic or molecular adhesive forces at points of actual contact

Step 1: The classical theory said friction was due to interlocking of surface irregularities (roughness). Step 2: However, the classical theory had drawbacks — it could not explain why extra-smooth surfaces have MORE friction. Step 3: The modern theory states that the area of actual contact is much smaller (ratio 1:10⁴) than apparent contact area. Step 4: At actual contact points, molecules come very close, forming strong adhesive bonds called 'cold welds'. Step 5: Breaking these cold welds requires force — this is what we call friction. Gravitational attraction and electromagnetic repulsion a