Four blocks of the same mass m connected by cords are pulled by a force F on a smooth horizontal surface as shown in Determine the tensions `T_1 ,T_2` and `T_3` in the cords.

Options

A. `T_(1)=(1)/(4)F,T_(2)=(3)/(2)F,T_(3)=(1)/(4)F`
B. `T_(1)=(1)/(4)F,T_(2)=(1)/(2)F,T_(3)=(1)/(2)F`
C. `T_(1)=(3)/(4)F,T_(2)=(1)/(2)F,T_(3)=(1)/(4)F`
D. `T_(1)=(3)/(4)F,T_(2)=(1)/(2)F,T_(3)=(1)/(2)F`

Answer

C

Explanation

( c) `T_(1)=((m_(2)+m_(3)+m_(4))F)/(m_(1)+m_(2)+m_(3)+m_(4))`
`therefore T_(1)=(3)/(4)F`
Similarly, `T_(2)=((m_(3)+m_(4))F)/(m_(1)+m_(2)+m_(3)+m_(4))`
`implies T_(2)(1)/(2)F`
`T_(3)=((m_(4))F)/(m_(1)+m_(2)+m_(3)+m_(4)) =(1)/(4)F`