Explore topic-wise InterviewSolutions in .

A circular hole in an aluminium plate is 1 cm in diameter at $0^{\circ }$. What is the diameter when the temperature of the plate is raised to ${100}^{\circ }$. (coefficient of linear expansion of aluminium $\alpha =2.55\times {10}^{-5}{/}^{\circ }$)

Mercury violet light $(\lambda =4558\stackrel{\circ }{A})$ is falling on a photosensitive material $(\varphi =2.5eV)$. The speed of the ejected electrons is in $m{s}^{-1}$, about

In the figure shown, find the acceleration of the block $B$. Assume all surfaces to be smooth.

Two rods of different materials having coefficients of thermal expansion ${\alpha }_1$ and ${\alpha }_2$ and Young's modulii $Y_1$ and $Y_2$ are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg $m^2.$ It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 $m{s}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is

A beaker of circular cross-section of radius $5\text{cm}$ is filled with mercury upto a height of $15\text{cm}$. Find the force exerted by the mercury on the bottom of the beaker. Take atmospheric pressure $={10}^5{\text{N/m}}^2$, density of mercury $=13600{\text{kg/m}}^3$, and $g=10{\text{m/s}}^2$.

We have an isolated conducting spherical shell of radius $10cm$. Some positive charge is given to it so that resulting electric field has a maximum intensity of $1.8\times {10}^{6}N{C}^{-1}.$ The same amount of negative charge is given to another isolated conducting spherical shell of radius $20cm$. Now, first shell is placed inside the second so that both are concentric as shown in the figure.



The electric potential at any point inside the first shell is

Two identical square rods of metal are welded end to end as shown in figure $\left(a\right)$, $20\text{calories}$ of heat flows through it in $4\text{minutes}$. If the rods are welded as shown in figure $\left(b\right)$, the same amount of heat will flow through the rods in

Find the work done by external agent in moving a $1C$ charge from point P to Q in presence of an infinitely long uniformly charged line of linear charge density $\lambda$ as shown.

A constant force $\overrightarrow{F}=(\hat{i}-2\hat{j}+\hat{k})\text{N}$ is acting on a body to displace it from $(0,1,1)\text{m}$ to $(0,-2,3)\text{m}$, the amount of work done by force is

If vectors $\overrightarrow{A}=\cos wt\hat{i}+\sin wt\hat{j}$ and $\overrightarrow{B}=\cos wt/2\hat{i}+\sin wt/2\hat{j}$ are functions of time , then the value of $t$ at which they are orthogonal to each other is

By Huygen's wave theory of light, we cannot explain the phenomenon of

[CPMT 1989; AFMC 1993, 99; MP PET 1995, 2003;RPMT 2003; BCECE 2003; Pb PMT 2004]

Degree of freedom of unknown gas is $3$. The gas can be

A stone tied to a string is rotated with a uniform speed in a vertical plane. If mass of the stone is $m$, the length of the string is $r$ and the linear speed of the stone is $v$, when the stone is at its lowest point, then the tension in the string will be ($g=$ acceleration due to gravity)

A thin uniform disc of mass $M$ and radius $R$ has concentric hole of radius $r$. Find the moment of inertia of the disc about an axis passing through its centre and perpendicular to its plane.

A thin prism $P_1$ with angle $4^{\circ }$ and made from glass of refractive index 1.54 is combined with another prism $P_2$Made of glass of refractive index 1.72 to produce dispersion without deviation. The angle of prism $P_2$ is

If $\overrightarrow{A}+\overrightarrow{B}$ is a unit vector along y - axis and $\overrightarrow{A}=\hat{i}-\hat{j}+\hat{k}$, then what is $\overrightarrow{B}$?

When a current $I$ is set up in a wire of radius $r$, the drift velocity is $v_d$. If the same current is set up through a wire of radius $2r$ of same material, the drift velocity will be

If the excess pressure inside a soap bubble of radius $1\text{cm}$ is balanced by an oil

($\rho =0.8{\text{g/cm}}^3)$ column of height $2\text{mm}$, then the surface tension of soap solution will be

[Take $g=10{\text{m/s}}^2$]

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have magnitude $3$ each. $\overrightarrow{A}\times \overrightarrow{B}=-5\hat{k}+2\hat{i}$. Find angle between $A$ and $B$

A door $1.6\text{m}$ wide requires a minimum force of $1\text{N}$ to be applied at the free end to open or close it. The minimum force that is required at a point $0.4\text{m}$ away from the hinges for opening or closing the door is

An object is initially at a distance of $200\text{cm}$ from a plane mirror. If the mirror approaches the object at a speed of $15\text{cm/s}$, then after $8\text{sec}$ the distance between object and its image will be

A bar of length $L_0=3.77\text{m}$ is placed on two rigid supports as shown in the figure. As a result of rise in temperature by $32{}^{\circ }\text{C}$ , bar cracks at its centre and buckles upward as shown in the figure. The fixed distance between the supports is also $L_0=3.77\text{m}$ and coefficient of linear expansion of the bar is $25\times {10}^{-6}/{}^{\circ }\text{C}$. Find the rise $x$ of centre of the bar.

The end of a capillary tube with radius $r$ is immersed in water. Assuming the tube to be sufficiently long, calculate the heat energy produced when the water rises in the tube.

[Assume angle of contact = $0^{\circ }$ for glass-water system, $\rho =$ density of water, $T=$ surface tension of water]

A square coil $AECD$ of side $0.1\text{m}$ is placed in a magnetic field $B=2t^2$. Here, $t$ is in seconds and $B$ is in Tesla. The magnetic field is into the paper. At time $t=2\text{s}$, induced electric field in $DC$ is

Potential energy of a particle executing SHM along $X-$ axis is given by $U=10+2x+(x-3{)}^2\text{J}$. Find the angular frequency of SHM, if mass of the particle is $3\text{kg.}$

A small collar of mass $m$ is given an initial velocity of magnitude $v_o$ on the horizontal circular track fabricated from a slender rod. If the coefficient of kinetic friction is ${\mu }_k$, determine the distance travelled before the collar comes to rest. (Recognize that the frictional force depends on the net normal force).

A liquid can easily change its shape but solids cannot because

Two blocks of mass 4 kg and 6 kg are placed in contact with each other on a frictionless horizontal surface. If we apply a push of 5 N on the heavier mass, the force on the lighter mass will be

A particle A moves along a circle of radius $R=10cm$ so that its radius vector $\overrightarrow{r}$ relative to O rotates with constant angular velocity $\omega =0.2rad/s$. Find the magnitude of the velocity of the particle and its total acceleration.

A body $A$ is thrown vertically upward with the initial velocity $v_1$. Another body $B$ is dropped from a height $h$. Find how the distance $x$ between the bodies depends on the time $t$ if the body begin to move simultaneously.

Gravitational mass is proportional to gravitational

When a force is applied at one end of an elastic wire, it produces a strain $ϵ$ in the wire. If $Y$ is Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

Two blocks tied with a massless string of length $3\text{m}$ are placed on a table rotating at an angular speed $\omega =4\text{rad/s}$. The axis of rotation is $1\text{m}$ from the block having $1\text{kg}$ mass. Assume that the surface below $2\text{kg}$ block is smooth and that below the $1\text{kg}$ block is rough. Find the tension $\left(T\right)$ in the string and the frictional force$\left(f\right)$ acting on the $1\text{kg}$ block. Take $g=10{\text{m/s}}^2$

The angular speed of a flywheel making $120\text{revolutions /minute}$ is

A block rides on a piston that is moving vertically with simple hormonic motion. The maximum speed of the piston is $2\text{m/s}$. If maxmium acceleration of block during its motion is$a=10{\text{m/s}}^2$, then the amplitude of motion at which the block and piston separates is

When a 1.0 kg mass hangs attached to a spring of length 50 cm, the spring stretches by 2 cm. The mass is pulled down until the length of the spring becomes 60 cm. What is the amount of elastic energy stored in the spring in this condition, if g = $10m/s^2$

At what temperature does the rms speed of oxygen molecules equal the escape velocity of - (i) Earth, (ii) the Moon? Assume gravitational acceleration at the moon is 0.6g.

A graph for an ideal gas at constant volume is plotted by taking pressure along y - axis and centigrade temperature along x - axis as shown in the figure below. Find the x intercept of the graph.

Area of a parallelogram, whose diagonals are $3\hat{i}+\hat{j}-2\hat{k}and\hat{i}-3\hat{j}+4\hat{k}$ will be:

For the system shown in figure, find the speed with which the $12\text{kg}$ block will hit the ground. Take $g=10{\text{m/s}}^2$.

Two block of mass $m_A=10\text{kg}$ and $m_B=15\text{kg}$ are connected by a light inextensible string and placed on a smooth horizontal surface as shown in the figure. Find the value of tension force on block $A$, if force applied on block $B$ is $50\sqrt{3}\text{N}$ .

The work done to get $n$ smaller equal size spherical drops from a bigger size spherical drop of water is proportional to:

A particle moves along the path $ABCA$ with a constant speed starting from $A$. Part $BC$ is circular with centre at $A$. The magnitude of displacement (from $A$) versus time graph will be