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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 vertical hanging bar of length $l$ and mass $m$ per unit length carries a load of mass $M$ at lower end, its upper end is clamped to a rigid support. The tensile stress a distance $x$ from support is $(A \rightarrow$ area of cross-section of bar)
When a uniform wire of radius $r$ is stretched by a $2kg$ weight, the increase in its length is $2.00\, mm$. If the radius of the wire is $r/2$ and other conditions remain the same, the increase in its length is .......... $mm$
The breaking stress of a wire of length $L$ and radius $r$ is $5$ $kg - wt/{m^2}$. The wire of length $2l$ and radius $2r$ of the same material will have breaking stress in $kg - wt/{m^2}$
If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is
The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1m$ suspended from the top of a roof at one end with a load $W$ connected to the other end. If the cross sectional area of the wire is ${10^{ - 6}}{m^2},$ calculate the young’s modulus of the material of the wire
Under the same load, wire $A$ having length $5.0\,m$ and cross section $2.5 \times 10^{-5}\,m ^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0\,m$ and a cross section of $3.0 \times 10^{-5}\,m ^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be