An object with uniform density $\rho$ is attached to a spring that is known to stretch linearly with applied force as shown below.When the spring object system is immersed in a liquid of density $\rho_1$ as shown in the above figure, the spring stretches by an amount $x_1\left(\rho > \rho_1\right)$. When the experiment is repeated in a liquid of density $\left(\rho_2 < \rho_1\right)$, the spring stretches by an amount $x_2$. Neglecting any buoyant force on the spring, the density of the object is
KVPY 2011, Advanced
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water isView Solution
- 2A cylindrical block of area of cross-section $A$ and of material of density $\rho$ is placed in a liquid of density one-third of density of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is $g$, the spring constant of the spring is:View Solution
- 3Asphere of radius $R$ and made of material of relative density $\sigma$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $R/r$ will beView Solution
- 4Pressure at the bottom of a tank of water is $3P$, where $P$ is atmospheric pressure. If water is drawn out till the level of water is lowered by one fifth, then the pressure at the bottom of the tank isView Solution
- 5Water flows in a horizontal tube (see figure). The pressure of water changes by $700\; \mathrm{Nm}^{-2}$ between $\mathrm{A}$ and $\mathrm{B}$ where the area of cross section are $40\; \mathrm{cm}^{2}$ and $20\; \mathrm{cm}^{2},$ respectively. Find the rate of flow of water through the tube. ........ $\mathrm{cm}^{3} / \mathrm{s}$View Solution
(density of water $=1000\; \mathrm{kgm}^{-3}$ )
- 6Density of ice is $\rho $ and that of water is $\sigma $. What will be the decrease in volume when a mass $M$ of ice meltsView Solution
- 7A thin tube sealed at both ends is $100\, cm$ long. It lies horizontally, the middle $20\, cm$ containing mercury and two equal ends containing air at standard atmospheric pressure . If the tube is now turned to a vertical position, by what amount will the mercury be displaced ? (Given : cross-section of the tube can be assumed to be uniform) ........ $cm$View Solution
- 8Different heads are in Column - $\mathrm{I}$ and its formulas are given in Column - $\mathrm{II}$. Match them appropriately.View Solution
Column - $\mathrm{I}$ Column - $\mathrm{II}$ $(a)$ Velocity head $(i)$ $\frac{P}{{\rho g}}$ $(b)$ Pressure head $(ii)$ $h$ $(iii)$ $\frac{{{v^2}}}{{2g}}$ - 9An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4 \;\mathrm{cm}$ and $4.8 \;\mathrm{cm},$ respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:View Solution
- 10Alaminar stream is flowing vertically down from a tap of cross-section area $1$ $cm^2$. At a distance $10 $ $cm$ below the tap, the cross-section area of the stream has reduced to $1/2$ $cm^2$. The volumetric flow rate of water from the tap must be about ........ $litre/\min$View Solution