A body of mass 10kg rests on a rough inclined plane whose angle of tilt θ θ is variable. θ θ is gradually increased until the body starts to slide down the ...

Answer Details

To find the coefficient of limiting friction between the body and the inclined plane, we can use the following steps: 1. Draw a free-body diagram of the body on the inclined plane. 2. Resolve the forces acting on the body along the incline and perpendicular to the incline. 3. Write down the equation for the limiting friction force, which is equal to the product of the coefficient of friction and the perpendicular force acting on the body. 4. Set the limiting friction force equal to the force acting down the incline, which is equal to the component of the weight of the body along the incline. 5. Solve for the coefficient of friction. Given that the body starts to slide down the plane at an angle of 30 degrees, we know that the force acting down the incline is equal to the component of the weight of the body along the incline. We can use trigonometry to find this component, which is equal to mg*sin(30), where m is the mass of the body and g is the acceleration due to gravity. The perpendicular force acting on the body is equal to mg*cos(30), and the limiting friction force is equal to the coefficient of friction times this perpendicular force. Therefore, we can write: mu*mg*cos(30) = mg*sin(30) Solving for the coefficient of friction, we get: mu = sin(30)/cos(30) = tan(30) = 1/sqrt(3) Therefore, the coefficient of limiting friction between the body and the inclined plane is 1/sqrt(3), which is approximately 0.577.