A sample of a liquid has an initial volume of $1.5\,L$ . The volume is reduced by $0.2\,mL$ , when the pressure increases by $140\,kP$ . What is the bulk modulus of the liquid
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A cubical solid aluminium (bulk modulus $=-V \frac{ dP }{ dV }=70 GPa$ ) block has an edge length of $1 m$ on the surface of the earth. It is kept on the floor of a $5 km$ deep ocean. Taking the average density of water and the acceleration due to gravity to be $10^3 kg m ^{-3}$ and $10 ms ^{-2}$, respectively, the change in the edge length of the block in $mm$ is . . . . .
A wire of length $5 \,m$ is twisted through $30^{\circ}$ at free end. If the radius of wire is $1 \,mm$, the shearing strain in the wire is ..........,.
Two wires $A$ and $B$ of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of $A$ is $3/2$ times of that of wire $B$. The ratio of the forces produced in two wires will be
The ratio of diameters of two wires of same material is $n : 1$. The length of wires are $4\, m$ each. On applying the same load, the increase in length of thin wire will be
A uniform rod of mass $m$, length $L$, area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be
A rod of length $l$ and radius $r$ is joined to a rod of length $l/2$ and radius $r/2$ of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of $\theta°$, the twist angle at the joint will be
$Assertion :$ Hollow shaft is found to be stronger than a solid shaft made of same equal material.
$Reason :$ Torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same length and material.
Two wires of equal lengths are made of the same material. Wire $A$ has a diameter that is twice as that of wire $B$. If identical weights are suspended from the ends of these wires, the increase in length is