In the arrangement shown in figure, the string are light and intextensible. The surface over which blocks are placed is smooth. Find

(a) the accelrations of the block
(b) the tension in each string.

Options

A. `a = 8 m//s^2` , `T_1=12 N`, `T_2 = 12N`
B. `a = 4 m//s^2` , `T_1=12 N`, `T_2 = 8N`
C. `a = 4 m//s^2` , `T_1=24 N`, `T_2 = 8N`
D. `a = 4 m//s^2` , `T_1=24 N`, `T_2 = 24N`

Answer

B

Explanation

(a) Let a be the acceleration of each block and `T_(1) " and " T_(2)` be the tension, in the two strings as shown in figure.

Taking the three blocks and the two strings as the system.

Using `sum F_(x)=ma_(x)`
For 1 kg block, `F-T_(1)=(1)(a)" or " 14-T_(1)=(1)(2)=(2)`
`therefore T_(1)=14-2=12N`
For 4 kg block,` T_(2)=(4)(a)" " therefore T_(2)=(4)(2)=8N`