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A uniform heavy rod of mass $20\,kg$. Cross sectional area $0.4\,m ^{2}$ and length $20\,m$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $x \times 10^{-9} m$. The value of $x$ is
(Given. Young's modulus $Y =2 \times 10^{11} Nm ^{-2}$ અને $\left.g=10\, ms ^{-2}\right)$
When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $2\, cms$. The work required to be done by an external agent in stretching this spring by $5\, cms$ will be ......... $joule$ $(g = 9.8\,metres/se{c^2})$
Two rods of different materials having coefficients of linear expansion ${\alpha _1},\,{\alpha _2}$ and Young's moduli ${Y_1}$ and ${Y_2}$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If ${\alpha _1}:{\alpha _2} = 2:3$, the thermal stresses developed in the two rods are equally provided ${Y_1}:{Y_2}$ is equal to
A cube of metal is subjected to a hydrostatic pressure of $4\;GPa.$ The percentage change in the length of the side of the cube is close to.......$\%$
(Given bulk modulus of metal, $B =8 \times 10^{10}\, Pa$ )
Rod of constant cross-section moves towards right with constant acceleration. Graph of stress and distance from left end is given as in figure. If density of material of rod at cross section $1$ is $9$ $\frac{{gm}}{{c{m^3}}}$ . Find density at cross section $2$.
Two wires of same diameter of the same material having the length $l$ and $2l.$ If the force $ F$ is applied on each, the ratio of the work done in the two wires will be
A string of area of cross-section $4\,mm ^{2}$ and length $0.5$ is connected with a rigid body of mass $2\,kg$. The body is rotated in a vertical circular path of radius $0.5\,m$. The body acquires a speed of $5\,m / s$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is $\ldots . . \times 10^{-5}$. (Use Young's modulus $10^{11}\,N / m ^{2}$ and $g =10\,m / s ^{2}$ )
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 $= 2100\,MPa$ )