Density `rho`, mass m and volume V are related as `rho = m//V`. Prove that
`gamma = - (1)/(rho) (drho)/(dT)`.

A body of density rho floats with a volume V_(1) of its total volume V immersed in one liquid of density rho_(1) and with the remainder of volume V_(2) immersed in another liquid of density rho_(2)," ""where"" "rho_(1)gt rho_(2). Find the relative volumes immersed in two liquids.

A body of density rho is released gently on the surface of a layer of liquid of depth d and density rho'(rho' lt rho) . Show that it will reach the bottom of the liquid after a time. [(2 d rho)/(g(rho-rho'))]^(1//2) .

Two substances of densities rho_(1) and rho_(2) are mixed in equal volume and the relative density of mixture is 4 . When they are mixed in equal masses, the relative density of the mixture is 3. the values of rho_(1) and rho_(2) are:

A block of density rho_(1) floats in two immiscible liquids of density 4 rho and 2 rho , such that (1/4)^(th) portion is in liquid of density 4 rho and remaining liquid of density 2 rho ,then rho_(1) =_________ g/(cm)^3 (Given rho=0.8g/(cm)^3 )

A solid uniform ball having volume V and density rho floats at the interface of two unmixible liquids as shown in Fig. 7(CF).7. The densities of the upper and lower liquids are rho_(1) and rho_(2) respectively, such that rho_(1) lt rho lt rho_(2) . What fractio9n of the volume of the ball will be in the lower liquid.

Two circular discs A and B have equal masses and uniform thickness but have densities rho_(1) and rho_(2) such that rho_(1)gt rho_(2) . Their moments of inertia is

It has been observed that velocity of ripple waves produced in water ( rho) , and surface tension (T) . Prove that V^(2) prop T// lambda rho .

The linear mass density i.e. mass per unit length of a rod of length L is given by rho = rho_(0)(1 + (x)/(L)) , where rho_(0) is constant , x distance from the left end. Find the total mass of rod and locate c.m. from the left end.

Two spherical planets P and Q have the same uniform density rho, masses M_p and M_Q and surface areas A and 4A respectively. A spherical planet R also has uniform density rho and its mass is (M_P + M_Q). The escape velocities from the plantes P,Q and R are V_P V_Q and V_R respectively. Then

A body of density rho floats with volume V_(1) of its total volume V immersed in a liquid of density rho_(1) and with the remainder of volume V_(2) immersed in another liquid of density rho_(2) where rho_(1)gtrho_(2) . Find the volume immersed in two liquids. ( V_(1) and V_(2) ).