The pressure of a medium is changed from $1.01 × 10^5$ $Pa$ to $1.165 × 10^5$ $Pa$ and change in volume is $10\% $ keeping temperature constant. The Bulk modulus of the medium is
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An increases in pressure required to decreases the $200\,\,litres$ volume of a liquid by $0.004\%$ in container is ........... $kPa$. (Bulk modulus of the liquid $= 2100\,\,MPa$ )
In the given figure, two elastic rods $A$ & $B$ are rigidly joined to end supports. $A$ small mass $‘m’$ is moving with velocity $v$ between the rods. All collisions are assumed to be elastic & the surface is given to be frictionless. The time period of small mass $‘m’$ will be : [$A=$ area of cross section, $Y =$ Young’s modulus, $L=$ length of each rod ; here, an elastic rod may be treated as a spring of spring constant $\frac{{YA}}{L}$ ]
A wire elongates by $l$ $mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $mm$)
Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \,cm$, then how much is the elongation in steel and copper wire respectively? Given, $Y_{\text {steel }}=20 \times 10^{11} \,dyne / \ cm ^2$, $Y_{\text {copper }}=12 \times 10^{11} \,dy ne / \ cm ^2$
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
A spherical ball contracts in volume by $0.02 \%$, when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............. $Nm ^{-2}$
A uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal, unextended length $L.$ The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R,$ respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal
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 . . . . .