Which of the following expression correctly represents `T_(1)` and `T_(2)` if the system is given an upward acceleration by a pulling up mass A?

Options

A. `T_(1)=M_(A)(a-g)+M_(B)(a-g),T_(2)=M_(B)(a-g)`
B. `T_(1)=M_(A)(g-a)+M_(B)(g-a),T_(2)=M_(B)(g-a)`
C. `T_(1)=M_(A)(g+a)+M_(B)(g+a),T_(2)=M_(B)(g+a)`
D. `T_(1)=M_(A)(g+a),T_(2)=M_(B) (g+a)`

Answer

C

Explanation

The force diagram of system (A+B) is shown in figure.

Here, `T_(1)-(M_(A)+M_(B))=(M_(A)+M_(B))a`
`therefore " "T_(1)=(M_(A)+M_(B))g+(M_(A)+M_(B))a`
`" "=(M_(A)+M_(B))(g+a)`
The force diagram of body B,
`T_(2)-M_(b)g=M_(B)a`
`therefore" "T_(2)=M_(B)(g+a)`