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When a cylindrical tube is dipped vertically into a liquid, the angle of contact is ${140}^{\circ }$. When the tube is dipped with an inclination of ${40}^{\circ }$, then the angle of contact is:

For the system shown below, block $B$ is moving upward with an acceleration $a$. What will be the acceleration of block $A$, if the string is inextensible and pulleys are frictionless?

Q47.

What fraction of the volume of the can is taken up by the balls?

A kid of mass $50\text{kg}$ stands at the edge of a platform of radius $1\text{m}$ which can be freely rotated about its axis. The moment of inertia of the platform is $0.02{\text{kg-m}}^2$. The system is at rest. The kid throws a ball of mass $2\text{kg}$ horizontally to his friend (friend standing on the ground) in a direction tangential to the rim with a speed $10\text{m/s}$ as seen by his friend. The angular velocity with which the platform will start rotating in $\text{rad/s}$ is

The difference in the speeds of sound in air at $-5^{\circ }C,$ 60 cm pressure of mercury and ${30}^{\circ }C,$ 75 cm pressure of mercury is (velocity of sound in air at $0^{\circ }C$ is 332 m/s)

Two springs of equal lengths and equal cross-sectional areas are made of materials whose Young's modulii are in the ratio of $2:3$. They are suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

The angle made by the vector $A=\hat{i}+\hat{j}$ with x- axis is

Two parallel plate capacitors $\text{A}$ and $\text{B}$ with capacitance $1\mu \text{F}$ and $5\mu \text{F}$ are charged separately to the same potential of $100\text{V}$. Now, the positive plate of $\text{A}$ is connected to the negative plate of $\text{B}$. Find the total loss of electrical energy in the given system.

In given figure, pulley having radius, $r=1\text{m}$ and moment of inertia $I=2{\text{kgm}}^2$ about its axis of rotation. If $T_1=4\text{N}$ and $T_2=2\text{N}$ are the tension in the strings. Find the angular acceleration of pulley. (Take anti-clockwise rotation +ve)

The plate separation in a parallel plate condenser is $d$ and plate area is $A$. If it is charged to $V$ volt and battery is disconnected then the work done in increasing the plate separation to $2d$ will be

Calculate the amount of heat required to convert 1.00 kg of ice at -10°C at normal pressure to steam at 100°C. Specific heat capacity of ice = 2100 J kg⁻¹ K⁻¹ , latent heat of fusion of ice = 3.36 × 10⁵ J kg⁻¹ , specific heat capacity of water = 4200 J kg ⁻¹ K⁻¹ and latent heat of vaporization of water = 2.25 × 10⁶ J kg⁻¹

A body of mass m is accelerated to velocity v in time $t_1$. The work done by the force as a function of time t will be

A thermally insulated vessel contains two liquids at temperature $T_1$ and $T_2$ respectively and specific heats $C_1$ and $C_2$ separated by a non- conducting partition. The partition is removed and the difference between the initial temperature of either of the liquids and the temperature T established in the vessel turns out to be equal to half the difference between the initial temperature of the liquids. Determine the ratio $\frac{m_1}{m_2}$ (masses of the liquids).

1. 96

White light is incident normally on a glass plate $\left(\text{in air}\right)$ of thickness $500\text{nm}$ and refractive index of $1.5$. The wavelength $\left(\text{in nm}\right)$ in the visible region $\left(\text{400 nm-700 nm}\right)$ that is strongly reflected by the plate is

The DC voltage gain $\frac{V_0}{V_i}$ in the following circuit is given by

1. 20.35

The position of a particle as a function of time $t,$ is given by $x\left(t\right)=at+b{t}^2-c{t}^3$



Where, $a,b$ and $c$ are constants. When the particle attains zero acceleration, then its velocity will be-

A source of sound and detector are placed at the same place on ground. At t = 0, the source S is projected towards reflector with velocity $V_0$ in vertically upward direction and reflector starts moving down with constant velocity $v_0$. At t = 0, the vertical separation between the reflector and source is $H(>\frac{v_0^2)}{2g})$. The speed of sound in air is $v(\gg v_0)$. Take f_0 as frequency of sound waves emitted by source. Based on above information answer the following questions.

Wavelength of sound waves as received by detector before reflection at $t=\frac{V_0}{2g}$,is

The gravitational field due to a disc of mass $M$ and radius $R$ at a point located $x$ distance away from the centre of disc along the axis of disc is given by

A steel bar of 40 mm $\times$ 40 mm square cross-section is subjected to an axial compressive load of $200kN.$ If the length of the bar is $2m$ and $E$ = $200GPa,$ the contraction of the bar will be

A uniform thin rod of mass $M$ and length $L$ is hinged by a frictionless pivot at its end $O$, as shown in the diagram. A bullet of mass $m$ moving horizontally with a velocity $v$, strikes the free end of the rod and gets embedded in it. The angular velocity of the system about $O$, just after the collision is,

The gravitational field in a region is given by $\overrightarrow{E}=\left(5nk{g}^{-1}\right)\overrightarrow{i}+\left(12Nk{g}^{-1}\right)\overrightarrow{j}$ (a) Find the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin. (b) Find the potential at the points (12 m, 0) and (0,5 m) if the potential at the origin is taken to be zero. (c) Find th echange in gravitational potential energy if a particle of mass 2 kg is taken from the origin to the point (12 m, 5m). (d) Find the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m).

The position vector of a moving particle in $x-y$ plane can be represented as $\overrightarrow{r}=\left(2t\hat{i}+2t^2\hat{j}\right)m$, where $t$ represents the time instant. The rate of change of $\theta$ at time $t=2s$. (where $\theta$ is the angle which its velocity vector makes with positive $x-$axis)

A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R.$ The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2.$ Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

Find the correct pathway of movement of water in the given diagram of cells.

When the switch is closed, the net charge which flows from point A to B is

A stone is dropped into a well in which the level of water is below the top of the well. If v is the velocity of the sound then the time T after dropping the stone is.?