Final answer:
The minimum coefficient of static friction (μ(static)) required to prevent a block from sliding down an inclined plane when the string breaks is 'tan(theta)', corresponding to option (a).
Step-by-step explanation:
When a string holding a block on an inclined plane breaks, the minimum value of the coefficient of static friction (μ(static)) necessary to prevent the block from sliding down depends on the angle of incline (θ).
The component of the object's weight acting down the slope is given by w · sin(θ), where w is the weight of the object. The frictional force that prevents the block from sliding must at least equal this component, which is μ(static) · w · cos(θ). Setting these two equal to each other, we solve for μ(static) to obtain the minimum coefficient of static friction as μ(static) = tan(θ).
Therefore, the minimum coefficient of static friction that would prevent the block from sliding down the inclined plane when the string breaks is tan(θ), which corresponds to option (a).
The maximum angle of an incline above the horizontal for which an object will not slide down is given by the equation: θ = tan-1(μ), where μ is the coefficient of static friction.
Therefore, the minimum value of the coefficient of static friction, μ(static), that would prevent the block from sliding down the inclined plane is given by μ = tan(θ).
So the correct answer is a. tan(θ).