A wax candle floats vertically in a liquid of density twice that of wax. The candle burns at the rate of $4\ cm/hr$ . Then, with respect to the surface of the liquid the upper end of the candle will
fall at the rate of $4\ cm/hr$
fall at the rate of $2\ cm/hr$
rise at the rate of $2\ cm/hr$
remain at the same height
A solid cylinder of mass $m$ and volume $v$ is suspended from ceiling by a spring of spring constant $k$ . It has cross-section area $A$ . It is submerged in a liquid of density $\rho $ upto half its length. If a small block of mass $M_o$ is kept at the centre of the top, the amplitude of small oscillation will be
A cylindrical vessel filled with water upto the height $H$ becomes empty in time $t_0$ due to a small hole at the bottom of the vessel. If water is filled to a height $4H$ it will flow out in time
A spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_1 (\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous} = -kv^2 (k > 0)$. The terminal speed of the ball is
The velocity of small ball of mass $m$ and density $\rho $ when dropped in a container filled with glycerine of density $\sigma $ becomes constant after sometime. The viscous force acting on the ball in the final stage is
The velocity of a small ball of mass $M$ and density $d_1,$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $d_2,$ the viscous force acting on the ball will be