Mechanical Properties of Solids

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires…

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A.$ If the length of the first wire is increased by…

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring.…

Two blocks of masses $3\mathrm{kg}$ and $5\mathrm{kg}$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi\,}\times\,10^{2}Nm^{-2}$. What is the minimum radius of…

A steel wire of length $3.2m\left(Y_{S}=2.0\times\,10^{11}Nm^{-2}\right)$ and a copper wire of length $4.4m\left(Y_{C}=1.1\times\,10^{11}Nm^{-2}\right)$ , both of radius $1.4\mathrm{mm}$are connected end to end. When…

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to $T_{M}$ . If the Young's modulus of the material of the wire is…

A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14\mathrm{mm}$. The tensile stress developed in the wire under equilibrium state is $7\times\,10^{5}Nm^{-2}$. The value of…

The elastic potential energy stored in a steel wire of length $20m$ stretched through $2\mathrm{cm}$ is $80J.$The cross sectional area of the wire is _____$\mathrm{mm}^{2}.$(Given,$Y=2.0\times\,10^{11}Nm^{-2}$)

A certain pressure '$P$' is applied to $1$ litre of water and $2$ litre of a liquid separately. Water gets compressed to $0.01%$ whereas the liquid gets compressed to $0.03%$. The ratio of Bulk modulus of water to that…

The area of cross-section of a railway track is $0.01m^{2}.$ The temperature variation is $10^{\circ}C.$Coefficient of linear expansion of material of track is $10^{-5}C-1\circ\,.$The energy stored per meter in the…

Two persons pull a wire towards themselves. Each person exerts a force of $200 \mathrm{~N}$ on the wire. Young's modulus of the material of wire is $1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. Original length of the…

When a rubber ball is taken to a depth of _______$m$ in deep sea, its volume decreases by$0.5%$ (The bulk modulus of rubber $=9.8\times\,10^{8}Nm^{-2}$Density of sea water $=10^{3}\mathrm{kg}m^{-3}$,$g=9.8ms^{-2}$)