Three masses are connected as shown in figure on a horizontal frictionless surface and pulled by a force of 60 N. The tensions `T_1 and T_2` are in the ratio

Options

A. `1:1`
B. `1:5`
C. `1:4`
D. `4:5`

Answer

B

Explanation

Horizontal component of force
` = 60 cos 30^@ = 30 sqrt( 3 )N`

`a=(" force")/((3+12+15 ) )=( 30 sqrt(3))/( 30) = sqrt(3) m//s^2`
` therefore T_2` = mass pulled ` xx ` acceleration
` = (3 + 12 ) xx sqrt(3) = 15 sqrt(3) N and T_1 = 3 xx sqrt(3) = 3 sqrt(3) N`
` therefore (T_1)/(T_2) = (3 sqrt(3))/( 15 sqrt(3)) = (1)/(5)`