For a constant hydraulic stress on an object, the fractional change in the object's volume $\left( {\frac{{\Delta V}}{V}} \right)$ and its bulk modulus $(B)$ are related as
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An elevator cable can have a maximum stress of $7 \times 10^7\,N/m^2$ for appropriate safety factors. Its maximum upward acceleration is $1.5\,m/s^2$ . If the cable has to support the total weight of $2000\,kg$ of a loaded elevator, the minimum area of crosssection of the cable should be ....... $cm^2$ $(g = 10\,m/s^2)$
A structural steel rod has a radius of $10\,mm$ and length of $1.0\,m.$ A $100\,kN$ force stretches it along its length . Young's modulus of structural steel is $2 \times 10^{11}\,Nm^{-2}.$ The percentage strain is about ....... $\%$
A pendulum consisting of a small sphere of mass $m$ suspended by an inextensible and massless string of length $l$ is made to swing in a vertical plane. If the breaking strength of the string is $2mg$ , then the maximum angular amplitude of the displacement from the vertical can be ....... $^o$
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 $= 2100\,MPa$ )
A copper solid cube of $60\,\, mm$ side is subjected to a pressure of $2.5 \times 10^7\, Pa$. If the bulk modulus of copper is $1.25 \times 10^{11}\, N/m^2$, the change in the volume of cube is
Two wires are made of the same material and have the same volume. However wire $1$ has crosssectional area $A$ and wire $2$ has cross-section area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire $2$ by the same amount?
Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ............ $mm$
A cylindrical wire of radius $1\,\, mm$, length $1 m$, Young’s modulus $= 2 × 10^{11} N/m^2$, poisson’s ratio $\mu = \pi /10$ is stretched by a force of $100 N$. Its radius will become