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

Options

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

Answer

A

Explanation

`mg=2Tsin45^(@)`
`mg=sqrt(2T)`
`T_(1)costheta=Tcos45^(@)`
`T_(1)costheta=(T)/(sqrt(2))=(mg)/(2)`
`{`:.`T=(mg)/(sqrt(2))}`
Further, `Mg+Tcos45^(@)=T_(1)sintheta`
`T_(1)sintheta=Mg+(Mg)/(sqrt(2))(1)/(sqrt(2))`
`T_(1)sintheta=Mg+(mg)/(2)`
`tantheta=(Mg+(mg)/(2))/((Mg)/(2))=1+(2m)/(m)`