A railway carriage moves over a straight track with acceleration a. Passenger in the carriage drops a stone. What is the acceleration of the stone w.r.t. the carriage and the earth?

Explanation

When the ball is dropped inside the train, it falls freely under the effect of acceleration due to gravity g. So, with respect to the earth , the acceleration of the stone is equal to g. Correct option is (d) .
Inside the carriage of train , the ball has two acceleration: (i) horizontal acceleration a due to motion of train and (ii) acceleration due to gravity g acting vertically downwards . So, resultant acceleration is
`a.=sqrt(a^(2)+g^(2))`
So, the correct option is (a)