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.
What was the magnitude of instantaneous net acceleration at time `t_(1)//2`? Obtain answer in terms of `F, T` and `m`.

Options

A. `([T^(2)+8F^(2)]^(1//2))/m`
B. `([T+4F^(2)]^(1//2))/(2m)`
C. `([T^(2)+16F^(2)]^(1//2))/(4m)`
D. none of these

Answer

C

Explanation

At `t=t_1/v`
`v_1=a_1t_1/2=F/m t_1/2`
`a_C=v_1^2/l=F^2/m^2t_1^2/(4m^2l)(mlT)/F^2=T/(4m)`
Net acceleration `a=sqrt(a_C^2+a_t^2)`
`=sqrt((T/(3m))^2+(F/m)^2)=sqrt((T^2+16F^2)/(4m))`