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Each of the three blocks P, Q and R shown in figure have a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm² and Young modulus 2 x 10¹¹ N m^-2. Neglect friction. Find the longitudinal strain developed in each of the wires. Take g = 10 m s^-2.

A horizontal platform with an object placed on it is executing SHM in the vertical direction. The amplitude of oscillation is 2.5 cm. what must be the least period of these oscillations so that the object is not detached from the platform? Take g = 10 $m{s}^{-2}$

A student is standing at a distance of 50 metres from the bus. As soon as the bus begins its motion with an acceleration of $1m/s^{-2}$, the student starts running towards the bus with a uniform velocity $u$ . Assuming the motion to be along a straight road, the minimum value of $u$ , so that the student is able to catch the bus is

A satellite is revolving round the earth in circular orbit at some height above surface of earth. It takes $5.26\times {10}^3$ seconds to complete a revolution while its centripetal acceleration is $9.92m/s^2$ . Height of satellite above surface of earth is (Radius of earth $6.37\times {10}^6$ m)

Arrange these fundamental forces in order of their magnitude, if they act between two protons separated by a distance of $1fm$

$F_G$ is Gravitational force

$F_E$ is Electromagnetic force

$F_N$ is Strong Nuclear Force

The total vibrational energy of a particle in $\text{SHM}$ is $E$. Its kinetic energy at half the amplitude from mean position will be :

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved

A bullet with muzzle velocity $100\sqrt{2}\text{m/s}$ is to be fired at an angle of ${45}^{\circ }$ with the horizontal. Find the coordinates of bullet after $t=4\text{s}$, assuming bullet was initially at origin. Take $g=10{\text{m/s}}^2$.

A sinusoidal wave travelling in the positive direction on a stretched string has an amplitude $20\text{cm}$, wavelength $1.0\text{m}$ and wave velocity $5\text{m/s}$. At $x=0$ and $t=0$ , it is given that $y=0$ and $\frac{\partial y}{\partial t}<0$. Find the wave function $y(x,t)$

A wall has two layers $A$ and $B$, each made of different materials. Both the layers have the same thickness and cross secional area. The thermal conductivity of the material of $A$ is twice that of $B$. Under thermal equilibrium, the temperature difference across the wall is ${36}^{\circ }C$. The temperature difference across the layer $A$ is

Two waves represented by equation $y_1=A\sin (\omega t-kx+{\varphi }_1)$ and $y_2=A\sin (\omega t-kx+{\varphi }_2)$ are superimposed such that the amplitude of resultant wave is $A$. Find the phase difference between them.

Given: $({\varphi }_1>{\varphi }_2)$

30 people gather in a $10\text{m}\times 5\text{m}\times 3\text{m}$ room for a confidential meeting. The room is completely sealed off and insulated. Calculate the rise in temperature of the room in half an hour. Assume that the average energy thrown off by the body of a person is $2500\text{kcal/day}$, density of air is $1.2{\text{kg/m}}^3$ and specific heat capacity of air at constant volume is $0.24\text{kcal kg}{{}^{-1}}^{\circ }{\text{C}}^{-1}$.

[Neglect volume occupied by the people].

A cart is moving horizontally along a staight line with a constant speed $30\text{m/s}$. A bullet is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was fired, after the cart has moved $80\text{m}$. At what speed (relative to the cart), the bullet must be fired ? Take $g=10{\text{m/s}}^2$.

Six identical resistors each of value $1\Omega$ are joined to form a regular hexagon. Further six more resistors of the same value are connected between the six vertices and the centre of the hexagon. The equivalent resistance between any two vertices lying opposite to each other is

The pulley is given an acceleration $a_0=2{\text{m/s}}^2$ starting from rest. A cable is connected to a block $A$ of mass $50\text{kg}$ as shown. Neglect the mass of the pulley. If $\mu =0.3$ between the block and the floor, then the tension in the cable is:

A semi circular ring of radius $R$ as shown in figure has charge per unit length $\lambda ={\lambda }_o\cos \theta$. Electric dipole moment of this ring is

X-rays were discovered by?

The coefficient of apparent expansion of a liquid in a copper vessel is $C$ and in a silver vessel $S$. The coefficient of volume expansion of copper is ${\gamma }_C$. What is the coefficient of linear expansion of silver

Two resistors have resistances $R_{01}$ and $R_{02}$ at $0^{\circ }C$ and temperature co -efficient $\propto 1$ and $\propto 2$. Find the value of $\propto$ for their series combination.

A semicircular ring of radius R uniformly charged with chage Q is rotated with angular velocity $\omega$ about point P as shown in figure. Its magnetic dipole moment will be.

Length $l$ and Acceleration due to gravity $g$ are measured with $\pm 6\%$ and $\pm 4\%$ errors respectively. The percentage error in determination of the Time period of a simple pendulum will be,

A body starting from rest moving with uniform acceleration has a displacement of $16\text{m}$ in first $4\text{s}$ and $9\text{m}$ in first $3\text{s}$. the acceleration of the body is

A monochromatic beam of light passes from a denser medium into a rarer medium. As a result [CPMT 1972]

The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of $\sqrt{3gl}$. Find the angle rotated by the string before it becomes slack.

What is the SI unit of Stefan’s constant?

Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or II as shown in the figure. One of the blocks has thermal conductivity $K$ and the other, $2K$. The temperature difference between the ends along the $x$-axis is the same in both the configuarations. It takes $9\text{s}$ to transport a certain amount of heat from the hot end to the cold end in configuration I. The time to transport the same amount of heat in the configuration II is:-

A simple pendulum is suspended to roof of a car. The car is moved with uniform velocity ${}^{\prime }{v}^{\prime }$. If the string makes an angle ${}^{\prime }{\theta }^{\prime }$ with vertical, ${}^{\prime }{\theta }^{\prime }$ will be equal to :

An emf of $5\text{V}$ is produced by an inductor due to self inductance, when the current changes at a steady rate from $3\text{A}$ to $2\text{A}$ in $1\text{ms}$. The value of self inductance of inductor is

The the system in the figure is in equilibrium. The value of PR in terms of RQ is equal to

In the figure shown, find the velocity of the $3kg$ mass after $10s$ if the system is released from rest at $t=0$. (Take $g=10m/s^2$)

A light spring of force constant $K$ is held between two blocks of masses $m$ and $2m$. The two blocks and the spring system rests on a smooth horizontal floor. Now the blocks are moved towards each other compressing the spring by $x$ and then they are suddenly released. Then find the relative velocity between the blocks when the spring attains its natural length.

If the pressure amplitude of sound wave in a medium is tripled and the wavelength is doubled then the amplitude of displacement of the particles in the medium becomes $x$ times the initial value. The value of $x$ is

Find the tension $T_1$ in the string. Assume all surfaces to be smooth.

When a pressure of 100 atmosphere is applied on a spherical ball of rubber, then its volume reduces to $0.01\%$. The bulk modulus of the material of the rubber in $\frac{dyne}{c{m}^2}$ is

If the coefficient of friction between an insect and bowl is $\mu$ and the radius of the bowl is $R$. Then the maximum height to which the insect can crawl in the bowl is

In the non-uniform circular motion shown below, the magnitude of change in tangential acceleration of the particle is

What is the equivalent spring constant for the system shown below?

A machine gun fires a steady stream of bullets at the rate of $n$ per minute into a stationary target in which the bullets get embedded. If each bullet has a mass $m$ and arrives at the target with a velocity $v$, the average force on the target is

A chain is placed on a frictionless table with one fourth of it hanging over the edge. If the length of the chain is 2m and its mass is 4kg, the energy need to be spent to pull it back to the table is

Acceleration of the particle in a rectilinear motion is given as $a=4t+3$ in $\left(m/s^2\right)$. The velocity and displacement as a function of time $t$ respectively are

(Given that at $t=0,u=3m/s,x=0m$)

An elevator without a ceiling is ascending up with an acceleration of $5{\text{ms}}^{-2}$. A boy on the elevator shoots a ball in vertical upward direction from a height of $2\text{m}$ above the floor of elevator. At this instant the elevator is moving up with a velocity of $10{\text{ms}}^{-1}$, and the floor of the elevator is at a height of $50\text{m}$ from the ground. The initial speed of the ball is $15{\text{ms}}^{-1}$ with respect to the elevator. Consider the duration for which the ball strikes the floor of elevator in answering following questions. ($g=10{\text{ms}}^{-2}$)

The vibrations of a string of length $20\text{cm}$ fixed at both ends are represented by the equation $y=2\sin \left(\frac{\pi x}{5}\right)\cos \left(12\pi t\right)$, where $x$ and $y$ are in $\text{cm}$ and $t$ in $\text{sec}$. How many nodes are located along the string?

Find the least count of a screw gauge whose least count of linear scale is 1 mm and the circular scale is divided in 50 divisions and 2 entire rotations makes to 1 division on linear scale.