Motion In A Straight Line

Step 1: Understanding the purpose of a secondary mirror. - A reflecting telescope primarily uses a concave primary mirror to collect and focus light. - A secondary mirror is placed at an intermediate point to redirect the focused light to an eyepiece.
Step 2: Function of the secondary mirror. - The primary mirror focuses light inside the telescope tube, making it difficult to place an eyepiece directly. - The secondary mirror redirects the light outside the tube, allowing for convenient viewing. - This design is seen in the Cassegrain and Newtonian telescopes.
Step 3: Evaluating other Option. - (A) Reducing mechanical support problems → Incorrect. The secondary mirror is not primarily used for structural support. - (B) Removing spherical aberration → Incorrect. Spherical aberration is corrected by parabolic mirrors, not by the secondary mirror. - (C) Making chromatic aberration zero → Incorrect. Chromatic aberration is caused by lenses, but reflecting telescopes use mirrors, which naturally eliminate this issue.
Final Answer:

Step 1: Understanding the given conditions. Given: - - - - Speeds: , , and along , , and respectively.
Step 2: Compute the time taken for each segment. Using , Total time taken:
Step 3: Compute the average speed. Simplifying: Rewriting in terms of a common denominator:
Final Answer:

Step 1: Understand the motion of the point A. When the disc rolls without slipping, every point on the disc follows a cycloidal path. Point A starts at the topmost point of the disc and traces an arc during the motion.
Step 2: Displacement after half a rotation. When the disc completes half of its rotation, the point A will have traveled a horizontal distance equal to the arc length of half the disc. This arc length is equal to the circumference of the disc divided by two, which is . The displacement of point A is the distance it has moved in both horizontal and vertical directions, and these form the two sides of a right triangle.
Step 3: Calculating the displacement. The horizontal displacement is , and the vertical displacement is also . Using the Pythagorean theorem, the displacement is: However, we also have an additional displacement because of the rolling motion, which contributes to the total displacement. Hence, the total displacement is: Thus, the displacement of point A from its initial position is .