A block of mass M is held motionless on a frictionless inclined plane by means of a string attached to a vertical wall as shown in the drawing. -If the string breaks, what is the magnitude of the acceleration of the block as it slides down the inclined plane? A)zero m/s² B)g C)g cos $\theta$ D)g sin $\theta$ E)g tan $\theta$

Question

Quizplus · Accepted Answer

When the string breaks, the only force acting on the block is the force of gravity, which pulls the block down the incline.
The force of gravity can be resolved into two components: 
- The component perpendicular to the incline (Mg cosθ) which does not affect the motion of the block.
- The component parallel to the incline (Mg sinθ) which causes the block to accelerate down the incline.
To find the magnitude of this acceleration, we use the formula:
a = F/m
where F is the parallel component of the force of gravity, and m is the mass of the block.
So, a = (Mg sinθ)/M = g sinθ. 
Therefore, the correct answer is D.

A Block of Mass M Is Held Motionless on a Frictionless