A model rocket rests on a frictionless horizontal surface and is joined by a string of length `l` to a fixed point so that the rocket moves in a horizontal circular path of radius `l`. The string will break if its tensiion exceeds a value `T`. The rocket engine provides a thrust `F` of constant magnitude along the rocket's direction of motion. the rocket has a mass `m` that does not change with time. Answer the following questions based on the above passage.
Starting from rest at `t=0` at what later time `t_(1)` is the rocket travelling so fast that the string breaks. Ignnore any air resistance.

Options

A. `((2mlT)/F^(2))^(1//2`
B. `((mlT)/(F^(2)))^(1//2)`
C. `((mlT)/(2F^(2)))^(1//2)`
D. `((mlF)/(T^(2)))^(1//2)`

Answer

B

Explanation

`a_t=F/m`
`v=u+a_1t_1=0+F/mt_1`
`T=(mv^2)/limpliesT=m/l F^2/m^2impliest_1=sqrt((mlT)/F^2)`