If A and B moves with acceleration ‘a’ as shown in diagram, calculate acceleration of C with respect to B A.2aB.a √2C.3aD.4a

1. Break Down the Problem

To find the acceleration of point C with respect to point B, we first need to understand the motions of A and B. Both A and B are moving with acceleration 'a'. We will establish the relationship between the accelerations.

2. Relevant Concepts

• The acceleration of C with respect to B can be calculated using vector addition if A and B are moving in a constrained manner to C.
• The formula for relative acceleration is given by: $a_{C/B} = a_C - a_B$

3. Analysis and Detail

Assuming that A and B are moving in a similar direction:

1. Acceleration of B is $a_B = a$.
2. Assuming C's acceleration is influenced by both A and B, let’s denote $a_C$ depending on the configuration shown in the diagram.
3. If C accelerates more due to the combination of the motions of A and B, for example, if C's acceleration equals the sum of the two: $a_C = a + a$ Thus, $a_C = 2a$
4. Hence, the relative acceleration from B to C would be: $a_{C/B} = a_C - a_B = 2a - a = a$

If from another viewpoint C is accelerating at a vector influenced by both A and B (consider angles and vector directions), then we might get:

• To analyze geometrically (in two dimensions), if both movements create a hypotenuse, C could be experiencing $a_{C/B} = \sqrt{a^2 + a^2} = a\sqrt{2}$

4. Verify and Summarize

Given the nature of the vectors:

• If C is simpler than originally assessed, from parallel motion, then it follows that:
  • In linear analysis and assuming angle vectors in this scenario which, with resulting acceleration against resultant direction, logically leads to $C$ being like effectively acceleration of $2a$ or its adjusted configuration.

Final Answer

Considering the diagram and calculations, the acceleration of C with respect to B is: $\text{Final Answer: } 2a \text{ (if straightforward)} \text{ or } a\sqrt{2} \text{ if in terms of directional contributions.}$

If there is conflicting direction in acceleration contributions or a clearer picture, no direct answer is provided here thus summarize your options aligned on geometrical contributions based on vector settings accordingly:

• Correct choices then may be assessed as related, possibly indicating $\sqrt{2} a$ or simply directional combinations thereof. Without specific configurations as given, leave it at stated positional assumptions. Adjust according to diagrams where noted directly.