Properties Of Matter Practice Questions

Two blocks of mass $2 {\text{kg}}$ and $4 {\text{kg}}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0 \times 10^{-5}$ ${\text{m}}$ and Young's modulus of the metal is $2.0 \times 10^{11} {\text{N}} / {\text{m}}^2$. The longitudinal strain developed in the wire is $\;\frac{1}{\alpha \pi }$. The value of $\alpha$ is_____ [Use ${\text{g}}=10 {\text{m}} / {\ s}^2$ ) [31-Jan-2024 Shift 2]

Match List-I with List-II : List-IEM-Wave List-IIWavelengthRange (A) A force that restores an elastic body of unit area to its original state (I) Bulk modulus (B) Two equal and opposite forces parallel to opposite faces (II) Young's modulus (C) Forcesperpendiculareverywhere to the surface per unit area same everywhere (III) Stress (D) Two equal and opposite forces perpendicular to opposite faces (IV) Shear modulusChoose the correct answer from the options givenbelow :

A soap bubble is blown to a diameter of $7 {\text{cm}}$. $36960 {\text{erg}}$ of work is done in blowing it further. If surface tension of soap solution is $40 {\text{dyne}} / {\text{cm}}$ then the new radius is _______ ${\text{cm}}$. Take $: (\pi =\;\frac{22}{7})$.

An elastic spring under tension of $3 {\text{N}}$ has a lengtha. Its length is b under tension $2 {\text{N}}$. For its length $(3 a-2 b)$, the value of tension will be ________ ${\text{N}}$.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.In the light of the above statements, choose the correct answer from the options given below : [27-Jan-2024 Shift 2]

Mercury is filled in a tube of radius $2 {\text{cm}}$ up to a height of $30 {\text{cm}}$. The force exerted by mercury on the bottom of the tube is _______ ${\text{N}}$.(Given, atmospheric pressure $=10^5 {\text{Nm}}^{-2}$, density of mercury $=1.36 \times 10^4 {\text{kg}} {\text{m}}^{-3}, {\text{g}}=10 {\text{ms}}^{-2}$, $\pi =\;\frac{22}{7}$ )

Under the same load, wire A having length $5.0 {\text{m}}$ and cross section $2.5 \times 10^{-5} {\text{m}}^2$ stretches uniformly by the same amount as another wire B of length $6.0 {\text{m}}$ and a cross section of $3.0 \times 10^{-5} {\text{m}}^2$ stretches. The ratio of the Young's modulus of wire A to that of wire B will be: [31-Jan-2023 Shift 2]

A wire of length ' ${\text{L}}$ ' and radius ' ${\text{r}}$ ' is clamped rigidly at one end. When the other end of the wire is pulled by a force ${\text{f}}$, its length increases by ' ${\text{l}}$ '. Another wire of same material of length ' $2 {\text{L}}$ ' and radius ' $2 {\text{r}}$ ' is pulled by a force ' $2 {\text{f}}$. Then the increase in its length will be : [15-Apr-2023 shift 1]

The surface tension of soap solution is $3.5 \times 10^{-2} {\text{Nm}}^{-1}$. The amount of work done required to increase the radius of soap bubble from $10 {\text{cm}}$ to $20 {\text{cm}}$ is ________ $\times 10^{-4} {\text{J}}$. (take $\pi =22 / 7$ ) [11-Apr-2023 shift 2]

Two wires each of radius $0.2 {\text{cm}}$ and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is ______ $\times 10^{-6} {\text{m}}$. [Young's modulus for steel $=2 \times$ $10^{11} {\text{Nm}}^{-2}$ and ${\text{g}}=10 {\text{ms}}^{-2}$ [10-Apr-2023 shift 1]

Young's moduli of the material of wires ${\text{A}}$ and ${\text{B}}$ are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires ${\text{A}}$ and ${\text{B}}$ will be in the ratio of [Assume length of wires $A$ and $B$ are same] [10-Apr-2023 shift 2]

A steel rod has a radius of $20 {\text{mm}}$ and a length of $2.0 {\text{m}}$. A force of $62.8 {\text{kN}}$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11} {\text{N}} / {\text{m}}^2$. The longitudinal strain produced in the wire is ________ $\times 10^{-5}$ (25) [6-Apr-2023 shift 1]

For a solid rod, the Young's modulus of elasticity is $3.2 \times 10^{11} {\text{Nm}}^{-2}$ and density is $8 \times 10^3 {\text{kg}} {\text{m}}^{-3}$. The velocity of longitudinal wave in the rod will be. [31-Jan-2023 Shift 2]

A metal block of base area $0.20 {\text{m}}^2$ is placed on a table, as shown in figure. A liquid film of thickness $0.25 {\text{mm}}$ is inserted between the block and the table. The block is pushed by a horizontal force of $0.1 {\text{N}}$ and moves with a constant speed. If the viscosity of the liquid is $5.0 \times 10^{-3} {\text{Pl}}$, the speed of block is ______ $\times 10^{-3} {\text{m}} / {\ s}$. [29-Jan-2023 Shift 2]

Eight equal drops of water are falling through air with a steady speed of $10 {\text{cm}} / {\ s}$. If the drops collapse, the new velocity is :- [11-Apr-2023 shift 2]

Given below are two statements :Statements I : Pressure in a reservoir of water is same at all points at the same level of water.Statements II : The pressure applied to enclosed water is transmitted in all directions equally. In the light of the above statements, choose the correct answer from the options given below : [10-Apr-2023 shift 1]

A metal block of mass ${\text{m}}$ is suspended from a rigid support through a metal wire of diameter $14 {\text{mm}}$. The tensile stress developed in the wire under equilibrium state is $7 \times 10^5 {\text{Nm}}^{-2}$. The value of mass ${\text{m}}$ is _______ ${\text{kg}}$. (Take, $g=9.8 {\text{ms}}^{-2}$ and $\pi =\;\frac{22}{7}$ ) [6-Apr-2023 shift 2]

A wire of density $8 \times 10^3 {\text{kg}} / {\text{m}}^3$ is stretched between two clamps $0.5 {\text{m}}$ apart. The extension developed in the wire is $3.2 \times 10^{-4} {\text{m}}$. If ${\text{Y}}=8 \times 10^{10} {\text{N}} / {\text{m}}^2$, the fundamental frequency of vibration in the wire will be ________ Hz. [11-Apr-2023 shift 2]