A ball is released from rest and rolls down an inclined plane, as shown in the following figure, requiring 4 s to cover a distance of 100 cm along the plane : Which one of the following is the correct value of angle 0 that the plane makes with the horizontal? (g = 1000 cm/s2)

To find the angle θ, we first calculate the acceleration (a) of the ball using the equation of motion s = ut + ½at². Given the ball starts from rest (u = 0), covers a distance s = 100 cm in time t = 4 s, the equation simplifies to 100 = ½ × a × 4². Solving this gives 100 = 8a, so a = 12.5 cm/s². For an object rolling down an inclined plane, the acceleration is typically a = g sin θ. However, in standard physics problems of this type involving a 'rolling' ball (often a solid sphere), the acceleration is a = (5/7)g sin θ. Using the provided g = 1000 cm/s², we have 12.5 = (5/7) × 1000 × sin θ, which leads to sin θ = 12.5 / (5000/7) = 87.5 / 5000 = 1.75 / 100. If treated as a simple sliding block (a = g sin θ), sin θ = 12.5 / 1000 = 1/80. Given the options, the intended calculation is sin θ = a/g = 12.5/1000 = 1/80.