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A bottle has an opening of radius $a$ and length $b$. A cork of length band radius $\left( {a + \Delta a} \right)$ where $\left( {\Delta a < < a} \right)$ is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is $B$ and frictional coefficient between the bottle and cork is $\mu $ then the force needed to push the cork into the bottle is
The ratio of radii of two wires of same material is $2: 1$. If these wires are stretched by equal force, the ratio of stresses produced in them is $.............$
A uniform dense rod with non uniform young's modulus is hanging from ceiling under gravity. If elastic energy density at every point is same then young's modulus with $x$ will change as which of the shown graph
Two wires of same diameter of the same material having the length $l$ and $2l.$ If the force $ F$ is applied on each, the ratio of the work done in the two wires will be
A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha {/^o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by $\Delta \,TK$. Young’s modulus, $Y$, for this metal is
A wire suspended vertically from one end is stretched by attaching a weight $200 \,N$ to the lower end. The weight stretches the wire by $1 \,mm$. The elastic potential energy gained by the wire is ....... $J$
Find the depth of lake at which density of water is $1\%$ greater than at the surface. Given compressibility ........... $km$ . $K = 50\times10^{-6}/atm$ ?
When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one then the increase in length will be ........ $cm$
Two wires $A$ and $B$ of same material have radii in the ratio $2: 1$ and lengths in the ratio $4: 1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......