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A steel rod of length $1\text{m}$ is fixed between two walls. If the rod is heated from ${25}^o\text{C}$ to ${35}^o\text{C}$, the stress developed in the rod is expressed as $x\times {10}^7{\text{N/m}}^2$. Find the value of $x$.

(coefficient of expansion for steel is $2\times {10}^{-5}{/}^{\circ }C$, Young's modulus of steel is $2\times {10}^{11}{\text{N/m}}^2$)

A car A of mass $1500\text{kg}$ is travelling at $25{\text{m s}}^{-1}$ collides with another car B of mass $1000\text{kg}$ travelling at $15{\text{m s}}^{-1}$ in the same direction. After collision, the velocity of car A reduces to $20{\text{m s}}^{-1}$. Calculate the velocity of car B after the collision.

Difference in height between the liquid columns in the vertical arms is - [Take $g=10{\text{m/s}}^2$]

The maximum tensile stress at the section X-X shown in the figure below is

A uniform rope of mass $0.1\text{kg}$ and length $2.45\text{m}$ hangs from a ceiling. The time taken by a transverse wave to travel through the full length of the rope is

[Take $g=9.8{\text{m/s}}^2$]

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The parallel combination of two air filled parallel plate capacitors of capacitance $C$ and $nC$ is connected to a battery of voltage, $V$. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant $K$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is-

A rod of length $10\text{m}$ is placed in vertical direction. Then the rod is rotated by ${90}^{\circ }$ in clockwise direction. Find out the displacement of the $COM$ of the rod.

Three moles of an ideal gas are taken through a cyclic process $ABCA$ as shown in $T-V$ indicator diagram. The gas loses $2510\text{J}$ of heat in the complete cycle. If $T_A=100\text{K}$ and $T_B=200\text{K}$, the work done by the gas during the process $BC$ is (line AB if extended passes through origin)

What is the moment of Inertia of a uniform hollow sphere of mass $M$ and radius $R$, about its diameter

A gas in an airtight container is heated from ${25}^{\circ }C$ to ${90}^{\circ }C$. The density of the gas will:

( Consider there is a negligible expansion of container)

In the circuit shown in figure, the potential difference $V$ must be

The number of revolutions made by electron in one second in the $2^{nd}$ Bohr orbit of hydrogen atom is:

Which one of the following is smallest in size ?

Frequency is the function of density $\left(\rho \right)$, length $\left(a\right)$ and surface tension $\left(T\right)$. Then its value is ($k$ is a constant)

Which one of the following plots represents the variation of gravitational field on a particle with distance r due a thin spherical shell of radius R?

The radioactivity of
a sample is R₁ at a time T₁ and R₂ at a time T₂.
If the half-life of the specimen is T, the number of atoms that have
disintegrated in the time (T₂-T₁) is proportional to:

Four point masses $2\text{kg},3\text{kg},5\text{kg}$ and $7\text{kg}$ respectively are placed at the four corners $A,B,C$ and $D$ of a square of side $4\text{m}$. The position of $COM$ will be

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by

The Van Der Waal’s equation of state for some gases can be expressed as: $(P+\frac{a}{V^2})(V-b)=RT$

Where $P$ is the pressure, $V$ is the molar volume and $T$ is the absolute temperature of the given sample of gas and $a,b$ and $R$ are constants.



The dimensions of $a$ are

Two thermally insulated vessels 1 and 2 are filled with air at temperatures $(T_1,T_2)$, volume $(V_1,V_2)$ and pressure $(P_1,P_2)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

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