Two cyllinders of same cross-section and length $L$ but made of two material of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with $a$ length $L/2$ above the surface of the liquid. If $d_1 > d_2$ then:
$d$ $>$ $\frac{3}{4}$$ d$
$\frac{d}{2}$ $>$ $d_1$
$\frac{d}{4}$ $>$ $d_1$
$d$ $<$ $d_1$
A solid sphere of radius $r$ is floating at the interface of two immiscible liquids of densities $\rho_1$ and $\rho_2\,\, (\rho_2 > \rho_1),$ half of its volume lying in each. The height of the upper liquid column from the interface of the two liquids is $h.$ The force exerted on the sphere by the upper liquid is $($ atmospheric pressure $= p_0\,\,\&$ acceleration due to gravity is $g) $
A concrete sphere of radius $R$ has a cavity of radius $ r$ which is packed with sawdust. The specific gravities of concrete and sawdust are respectively $2.4$ and $0.3$ for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be
A wide bottom cylindrical massless plastic container of height $9 \,cm$ has $40$ identical coins inside it and is floating on water with $3 \,cm$ inside the water. If we start putting more of such coins on its lid, it is observed that after $N$ coins are put, its equilibrium changes from stable to unstable. Equilibrium in floating is stable if the geometric centre of the submerged portion is above the centre of the mass of the object). The value of $N$ is closed to
A boy carries a fish in one hand and a bucket(not full) of water in the other hand . If he places the fish in the bucket , the weight now carried by him (assume that water does not spill) :
Water flows out of the hole on the side of a bucket and follows a parabolic path. If the bucket falls freely under gravity, ignoring air resistance, the water flow