Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} {kg}$, The inner and outer radii of each column are $50\; {cm}$ and $100 \;{cm}$ respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use $\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]$
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A steel wire of diameter $0.5 mm$ and Young's modulus $2 \times 10^{11} N m ^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0 m$. A vernier scale with $10$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count $1.0 mm$, is attached. The $10$ divisions of the vernier scale correspond to $9$ divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $1.2 kg$, the vernier scale division which coincides with a main scale division is. . . . Take $g =10 m s ^{-2}$ and $\pi=3.2$.
The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line
Auniform rod rotating in gravity free region with certain constant angular velocity. The variation of tensile stress with distance $x$ from axis of rotation is best represented by which of the following graphs.
The upper end of a wire of radius $4\, mm$ and length $100\, cm$ is clamped and its other end is twisted through an angle of $30°$. Then angle of shear is ..... $^o$
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
The bulk modulus of rubber is $9.1 \times 10^8\,N/m^2$. To what depth a rubber ball be taken in a lake so that its volume is decreased by $0.1\%$ ? ....... $m$