A dumbbell is placed in water of density `rho`. It is observed that by attaching a mass `m` to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass `m` is negligible. The value of length `l` is

Options

A. `(d(Vrho-3m))/(2(Vrho-2m))`
B. `(d(Vrho-2m))/(2(Vrho-3m))`
C. `(d(Vrho+2m))/(2(Vrho-3m))`
D. `(d(Vrho-2m))/(2(Vrho+3m))`

Answer

B

Explanation

Taking torque about m.
`(B-Mg)(d-l)=(B-2Mg)l`
`((V)/(2)rhog-2Mg)(d-l)=((V)/(2)rhog-2Mg)l`
`((V)/(2)rhog-Mg)d-((V)/(2)rhog-Mg)l=((V)/(2)rhog-2Mg)l`
`((v)/(2)rhog-Mg)d=(Vrhog-3Mg)l`
`l=(((V)/(2)rhog-Mg))/((Vrhog-3Mg))" "impliesl=(Vrho-2M)/(2(Vrho-2M))`