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A square of side $2.5\text{cm}$ is cut out from a circular disc of radius $10\text{cm}$ as shown in the figure. Take the origin at the centre of the circular disc. What will be the coordinates of the centre of mass of this new shape with respect to the origin? Consider the material used to be of uniform density.

On heating a liquid of coefficient of cubical expansion g in a container having coefficient of linear expansion $\frac{g}{3}$, the level of liquid in the container will

Find the ratio of specific gas constant for $H_2$ to the specific gas constant for $O_2$?

Two shells have been fired from cannon $A$ and $B$ simultaneously at $t=0$ with velocity as shown in the figure. Find the time when both shells collide in air, given that horizontal distance between cannons is $30\text{m}$.

The $\text{SI}$ unit of density is

The unit vector which is perpendicular to the vectors $\overrightarrow{A}=\hat{i}+2\hat{j}-\hat{k}$ and $\overrightarrow{B}=3\hat{i}-2\hat{j}+\hat{k}$ is

Unpolarized light with an intensity of $I_0=16\frac{W}{m^2}$ is incident on a pair of polarizers. The first polarizer has its transmission axis aligned at ${50}^{\circ }$ from the vertical. The second polarizer has its transmission axis aligned at ${20}^{\circ }$ from the vertical.



What is the intensity of the light when it emerges from the second polarizer?

A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position. This stretches the spring by a length $d$. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case?

A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11\text{km/s}$, the escape velocity from the surface of the planet would be

A boy and a block, both of same mass $m\text{kg}$, are initially at the same horizontal level and attached to a frictionless pulley through a light inextensible string that moves over the frictionless pulley as shown in figure. The boy starts moving upward with an acceleration of $5{\text{m/s}}^2$ relative to the rope. If the block has to travel a total distance of $10\text{m}$ before reaching at the level of pulley, the time taken by the block in doing so is equal to

A sphere of mass $1\text{kg}$ rests at one corner of a box. The box is then moved with a velocity $\overrightarrow{v}=8t\hat{i}-2t^2\hat{j}$. Where $t$ is time in second. The force by sphere on the box at $t=1\text{s}$ is ($g=10{\text{ms}}^{-2}$) [Figure shows vertical plane of the box]

Two slits in Young's experiment have widths in the ratio 1 : 25. The ratio of intensity at the maxima and minima in the interference pattern, $\frac{I_{max}}{I_{min}}$ is

A ball thrown by one player reaches the other in 2 sec. the maximum height attained by the ball above the point of projection will be about

A force varying with displacement$\left(x\right)$ is given as $F=a{e}^{-bx}$ acts on a particle of mass $m$ moving in a straight line. Find the work done on the particle in its displacement from origin to a distance $d$.

A source of sound S and a detector D are placed at some distance from one another. A big cardboard is placed near the detector and perpendicular to the line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is $336\frac{m}{s}$?

Consider the situation shown in figure. Initially the spring is unstretched when the system is released from rest. Assuming no friction in the pulley, find the maximum elongation of the spring?

A steel wire of length $1\text{m}$ and cross sectional area $A$ is stretched by $1\text{cm}$ under a given load. When the same load is applied to another steel wire of double length and half the cross-sectional area of the first one, the amount of stretching (extension) is

Which of the following do not depend on frame of reference?

1. Mass

2. Distance between two points

3. Velocity

4. Distance

The motion of a particle along a straight line is described by the equation $x=6+27t-t^3$.

Find the time when $K.E$ of the particle is zero.

A source emitting sound of frequency $90\text{Hz}$ is placed in front of a wall at a distance $3\text{m}$ from it. A detector is also placed in front of the wall at the same distance from it as shown in the figure. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air = $360{\text{ms}}^{-1}$.

Two small identical balls P and Q, each of mass $\frac{\sqrt{3}}{10}$ gram, carry identical charges and are suspended by threads of equal lengths. At equilibrium, they position themselves as shown in Fig. 20.5 what is the charge on each ball. Given $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N{m}^2{C}^{-2}$ and take $g=10N/Kg.$

Why couldn't the mysterious rays coming out of Beryllium foil in Chadwick's experiment on being hit by alpha particles have been gamma rays?

The effective resistance between the points $P$ and $Q$ of the electrical circuit shown in the figure is

Two balls of different masses $m_a$ and $m_b$ are dropped from two different heights $a$ and $b$. The ratio of time taken by the two to drop through these distances is

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

The mass of a bucket containing water is 10 kg. What is the work done in pulling up the bucket from a well of depth 10 m if water is pouring out at a uniform rate from a hole in it and there is loss of 2kg of water from it while it reaches the top $(g=10m/se{c}^2)$

A ball is dropped from a of height $80\text{m}$. It hits the ground and rebounds with half the speed before collision. Draw its velocity-time graph.

A body of mass $2\text{kg}$ slide down a curved track which is quadrant of a circle of radius $2\text{m}$. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is

$(g=10{\text{m/s}}^2)$

Two successive resonance frequencies in an open organ pipe are $1800\text{Hz}$ and $2600\text{Hz}$. Find the length of the tube if the speed of sound in air is $340\text{m/s}$.

The work function of a photoelectric material is 4.0 eV. What is the threshold wavelength?

Fluid used in the column is mercury. The pressure of the gas in the cylinder is :

Given : Atmospheric pressure $=1.01\times {10}^5{\text{N/m}}^2,g=10{\text{m/s}}^2$ and density of mercury $=13600{\text{kg/m}}^3$.

If a capacitor of $10\mu F$ is charged to 10V and then connected to a new circuit to discharge through a $10\Omega$ resistor, what is the charge on it after $20\mu s$?

The space between two large horizontal metal plates 6cm apart is filled with a liquid of viscosity $0.8Ns/m^2$ . A thin planck of surface area $1m^2$ is moved parallel to the length of the plates such that the planck is at a distance of 2cm from one plate and 4cm from the other.The force F required to drag it with a constant speed of is $1m{s}^{-}1$ is

Evaluate: $\int (3e^{3x}+e^{-x})dx$

Two plane mirrors A and B are aligned parallel to each as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value $a_0$ at the end of $100$ oscillations. When the oscillator completes $200$ oscillations, its amplitude must be

A charge (q, m) is projected perpendicular away from an infinitely long wire carrying a current i with a speed $v_0$. Find the maximum separation between the charge and the wire in the subsequent motion if the initial separation is $x_0$.

A car is moving in a circular horizontal track of radius $10\text{m}$ with a constant speed of $10{\text{ms}}^{-1}$. A plumb bob is suspended from the roof of the car by a string of length $1\text{m}$. The angle made by the string with the vertical is $(g=10{\text{ms}}^{-2})$

Two sinusoidal plane waves of the same frequency having intensities $I_0$ and $4I_0$ are travelling in the same direction. The resultant intensity at a point at which the waves meet with a phase difference of $\frac{\pi }{2}$ is

Twelve wires, each having equal resistance of 2 $\Omega$, are joined to form a cube. Equivalent resistance between the ends of a face diagonal is.

A refrigerator whose coefficient of performance is $5$, extracts heat from the cooling compartment at the rate of $250\text{J/cycle}$. Find the amount of heat discharged per cycle to the room.

The temperature of water at the surface of a deep lake is $2^{\circ }C$. The temperature expected at the bottom is.(Lake is deep enough)

If a force $\overrightarrow{F}=(7\hat{i}-6\hat{j}+2\hat{k})\text{N}$ and velocity $\overrightarrow{v}=(6\hat{i}+\hat{k})\text{m/s},$ then the instantaneous power is

A plane electromagnetic wave of wave intensity 6 $W/m^2$strikes a small mirror area 40 $c{m}^2$, held perpendicular to the approaching wave. The momentum transferred by the wave to the mirror each second will be

A $10\text{kg}$ block placed on a rough horizontal floor is being pulled by a constant force $F=100\text{N}$ acting at angle ${37}^{\circ }$. The coefficient of kinetic friction between the block and the floor is $0.4$. Find the total work done on the block over the displacement of $5\text{m}$.

A $50\text{kg}$ person stands on a $25\text{kg}$ platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the figure. The platform moves upward at a steady rate if the force with which the person pulls the rope is

Find out the dimensions of the constants a and b in the Vander Waal's equation $[p+\frac{a}{v^2}](V-b)=RT$

where p is pressure, v is volume, R is gas constant and T is temperature.

$\begin{array}{cc}Column-I& Column-II\\ a& \left(i\right)\left[M{L}^5{T}^{-2}\right]\\ b& \left(ii\right)\left[M^2{L}^3{T}^{-1}\right]\\ & \left(iii\right)\left[M^0{L}^3{T}^0\right]\\ & \left(iv\right)\left[M^0{L}^2{T}^{-1}\right]\end{array}$

An aeroplane flying 490 m above ground level at 100 m/s, releases a block. How far on ground will it strike

A particle moves along a semicircle of radius $10\text{m}$ in 5 seconds. The average velocity of the particle is