An inclined plane makes an angle 30° with horizontal. A solid sphere rolling down this inclined plane has a linear acceleration of

We can look at the forces acting on the sphere to find the linear acceleration of a solid sphere rolling down an inclined plane set at an angle of 30 degrees with the horizontal. The main forces are the gravitational force, which is the cause of the motion of the sphere, and the frictional force, which is required for rolling motion.

When the sphere rolls down the incline, gravity pulls it down, but the angle of the incline determines how this force is distributed. The gravitational force can be divided into two components: one that acts parallel to the slope, propelling the sphere downwards, and another that acts perpendicular to the slope, influencing the normal force experienced by the sphere.

As the sphere rolls without slipping, it is undergoing both translation and rotation simultaneously. The resulting linear acceleration would then be developed from the motion dynamics of a rolling sphere.

For a solid sphere rolling on a 30-degree incline, the acceleration in the line of motion ends up being just some fraction of g, weighted by the sine of the angle of inclination. In this problem, the specified conditions allow calculating the acceleration as the sphere rolls down the ramp to be 5g/14, so this is the right solution.

Click here for more:- https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/