A circular hole of diameter $\mathrm{d}=10\mathrm{cm}$ is to be punched out of a plate having an ultimate shearing stress, ${\sigma }_{\mathrm{s}}=2\times {10}^8\mathrm{pa}$ as shown in the figure. If the maximum compressive strength on the punch is limited to ${\sigma }_{\mathrm{c}}=4\times {10}^8\mathrm{pa},$ determine the maximum thickness 't' of the plate.

 

Consider two identical rods $\mathrm{A}$ and $\mathrm{B}$ with the applied forces as shown. They are lying on a smooth surface and made of the same material. Which of the following is wrong?

A ring of radius $R$ is made of a thin wire of material of density $\rho$, having cross-sectional area '$a$' and Young's modulus $Y$. The ring rotates about an axis perpendicular to its plane and through its centre. Angular frequency of rotation is $W$. The ratio of kinetic energy to potential energy is

A uniform ring of mass $m$ with the outside radius $r_2$ is fitted tightly on a shaft of radius $r_1$. The shaft is rotated about its axis with a constant angular acceleration $\beta .$ The moment of elastic forces in the ring as a function of the distance $r$ from the axis of rotation is

Two wires of same material are hanging as shown in the figure. Breaking stress is equal for both the wires.

Assertion: If mass '${\mathrm{m}}_2$' increases, then upper wire will break first.

Reason: Breaking load of two wires of same material can be different.

A uniform bar of square cross-section is lying along a frictionless horizontal surface. A horizontal force is applied to pull it from one of its ends. Then,

A light rod of length $200 \mathrm{cm}$ is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its end. One of the wires is made of steel and has area of cross-section $0.1$ ${\mathrm{cm}}^2$ and the other of brass of cross-sectional area $0.2 {\mathrm{cm}}^2.$ An object of mass $\mathrm{m}$ is hung to the rod. $\left({\mathrm{Y}}_{\text{steel }}=2\times {\mathrm{Y}}_{\text{brass }}\right)$

At which distance from one end of the rod should a weight be hung to produce equal strains in both the wires?

A steel wire of diameter $d=1\mathrm{mm}$ is stretched horizontally between $2$ clamps located at distance $l=2 \mathrm{m}$ from each other. A weight of mass $\mathrm{m}=0.25 \mathrm{kg}$ is suspended from midpoint $O$ of the wire. What will the resulting descent of the point $\mathrm{O}$ be in $\mathrm{cm}$? (Here, the modulus of elasticity of steel is $E_{\mathrm{steel}}=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^2$)

In the determination of Young's modulus of elasticity of a wire, a force is applied and extension is recorded. Initial length of wire is $1 \mathrm{m}$. The curve between extension and stress is depicted, then Young's modulus of wire will be: