Question

If A is moving with an acceleration of 1m per second squared the acceleration of block B with respect to ground will be how much?

Answer 1

Acceleration of b will be equal to 1 m/s*s towards right and 1 m /s*s towads downward.
Because B is attached to A so it will move with A with same acceleration towards right and also it will move downward with same acceleration because when A move the string also moves and string is tight .

Hence magnitude of acceleration of B would be square root 2.