The surface are frictionless, the ratio of `T_(1)` and `T_(2)` is

Options

A. `sqrt(3):1`
B. `1: sqrt(3)`
C. `1:5`
D. `5:1`

Answer

D

Explanation

(d)
`T_(2)=(m_(1)F cos 30^(@))/(m_(1)+m_(2)+m_(3))=(3F cos 30^(@))/(3+12+15)`
`(3F cos 30^(@))/(30)=(F cos 30^(@))/(10)`
`T_(1)=((m_(1)+m_(2))F cos 30^(@))/(m_(1)+m_(2)+m_(3))`
`((3+12) F cos 30^(@))/(3+12+15)=(15 F cos 30^(@))/(30)=(F cos30^(@))/(2)`
The ratio between `T_(1) " and " T_(2)`
`T_(1):T_(2)=( F cos 30^(@)//2)/(F cos 30^(@)//10)=5:1`