The bulk modulus of rubber is $9.1\times 10^8\,N/m^2$. To ......... $m$ depth a rubber ball be taken in a lake so that its volume is decreased by $0.1\,\%$ .
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A $0.1 \mathrm{~kg}$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \mathrm{~m}$ and its crosssectional area is $4.9 \times 10^{-7} \mathrm{~m}^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \ \mathrm{rad} \mathrm{s}^{-1}$. If the Young's modulus of the material of the wire is $\mathrm{n} \times 10^9 \mathrm{Nm}^{-2}$, the value of $\mathrm{n}$ is
Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of
A wooden wheel of radius $R$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross section area $S$ and length $L$. $L$ is slighly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel.As it cools down to surronding temperature, it presses the semicircular parts together. If the coefficint of linear expansion of the metal is $\alpha$, and its young's modulus is $Y$, the force that one part of wheel applies on the other part is
A cube of aluminium of sides $0.1\, m$ is subjected to a shearing force of $100\, N$. The top face of the cube is displaced through $0.02 \,cm$ with respect to the bottom face. The shearing strain would be