Two masses `m` and `M` are attached with strings as shown. For the system to be in equilibrium we have.

Options

A. `tan theta=1+(2M)/(m)`
B. `tan theta=1+(2m)/(M)`
C. `tan theta=1+(M)/(2m)`
D. `tan theta=1+(m)/(2M)`

Answer

A

Explanation

(a) `2T_(1) cos 45^(@)=mg`
`therefore" " T_(1)=(mg)/(sqrt(2))`….(i)

`T^(2) cos theta=(T_(1))/(sqrt(2))=(mg)/(2),T_(2) sin theta=mg +(mg)/(2)`
`tan theta =(mg+(mg)/(2))/((mg)/(2))=1+(2M)/(m)`