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A man $X$ can hear only upto 10 kHz and another man $Y$ upto 20 kHz. A note of frequency 500 Hz is produced before them from a stretched string. Then

The pressure of the gas in a constant volume gas thermometer at steam point (373.15K) is $1.5\times {10}^{4}Pa$. What will be the pressure at the triple point of water ?

The electric field in a region is given by

$E=(2\hat{i}+3\hat{j})\times {10}^{3}N{C}^{-1}$

The electric flux through a rectangular surface $10cm\times 20cm$ held parallel to the y-z plance is

Block $A$ with a kinetic energy of $500\text{J}$ collides with another block $B$ of mass $10\text{kg}$ initially kept at rest. Assuming that the collision is perfectly elastic, what is the final speed of the block $B$?

An ideal monoatomic gas is taken around the cycle $ABCD$ as shown in figure below. Work done during the cycle is

The sum of the magnitudes of two forces is $18\text{N}$ and the magnitude of their resultant is $12\text{N}$. If the resultant makes an angle of ${90}^{\circ }$ with the smaller force, then find the magnitude of the forces.

A mercury Celsius thermometer is transferred from melting ice to a hot liquid. The mercury rises to $\frac{9}{10}$th of the distance between the two fixed points. Find the temperature of the liquid in Fahrenheit scale.

Two particles $A$ and $B$ are projected simultaneously from the towers of same height as shown in the figure with velocities $V_A=20\text{m/s}$ and $V_B=10\text{m/s}$ respectively. They collide in air after 0.5 seconds. Find '$x$'.

The volume charge density as a function of distance $x$ from one face inside a unit cube is varying as shown in the figure. Then the total flux (in S.I. units) through the cube if $({\rho }_o=8.85\times {10}^{–12}\frac{C}{m^3})$ is :

A cylinder of mass 5 kg and radius 4 m is rolling purely on a horizontal surface. What will be the angular momentum of the cylinder with respect to any point on the ground if its centre of mass moves with the velocity of 20 m/s?

The P-V diagram of 2 gm of helium gas for a certain process A $\to$ B is shown in the figure. what is the heat given to the gas during the process A $\to$ B

The displacement of a particle moving in a straight line is described by the relation $x\text{(in m)}=6+12t-2t^2$. The distance covered by the particle in first $5\text{s}$ is

A boy runs for $10\text{min}$ at a uniform speed of $9\text{km/h}$. At what speed should be run for the next $20\text{min},$ so that the average speed comes to $12\text{km/h}$?

The position of a particle is given by $\overrightarrow{r}=3t\hat{i}+\sqrt{3}{t}^2\hat{j}-4\hat{k}$ where $t$ is in seconds and $\overrightarrow{r}$ is meters. Find out magnitude of velocity $\overrightarrow{v}$ and angle made by velocity $\overrightarrow{v}$ with X-axis at $t=\sqrt{3}\text{s}.$

A proton and a deutron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deutron on circular path of radius $R_p$ and $R_d$ respectively, the correct statement is

A particle initially at rest, moves along x-axis, such that its acceleration varies with time t as a = (4t + 5) m/s². If it starts from origin, then distance travelled by particle in 2 second will be



एक कण प्रारम्भ में विराम में है, यह x-अक्ष के अनुदिश इस प्रकार गति करता है कि इसका त्वरण, समय t के साथ a = (4t + 5) m/s² के अनुसार परिवर्तित हो। यदि यह मूल बिन्दु से गति प्रारम्भ करता है, तब 2 सेकण्ड में कण द्वारा तय की गई दूरी होगी

One end of a long metallic wire of length $L$ is tied to the ceiling. The other end is tied to a massless spring of spring constant $k$. A mass $m$ hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are $A$ and $Y$ respectively. If the mass is slightly pulled down and released, it will oscillate with a time period $T$ equal to

[Assume that , within the elastic limit, wire behaves as a spring]

A stone is projected from the ground with a velocity $50\text{m/s}$ at an angle of ${30}^{\circ }$. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground ($g=10{\text{m/s}}^2$)

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

A disc of radius $R$ uniformly charged with a charge $Q$ is rotated at angular velocity ${}^{\prime }{\omega }^{\prime }$ about an axis passing through its center and perpendicular to plane disc. Net magnetic field at center of disc is.

Avinash travels half the distance from his home to office at speed of 15 km/hr and rest of the journey at 30 km/hr. Find the average speed of Avinash on his way to office.

A particle of mass $m$ is projected with velocity $v$ at an angle $\theta$ with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory.

In the shown figure a mass m slides down the frictionless surface from height h and collides with a uniform vertical rod of length L and mass M. After a collision, mass m sticks to the rod. The rod is free to rotate in a vertical plane about a fixed axis through O. Find the maximum angular deflection of the rod from its initial position

A boy throws a ball upwards with a velocity of $5\text{m/s}$ from a balloon descending with a constant velocity of $15\text{m/s}$. After how much time will the boy be able to catch the ball? Take $g=10{\text{m/s}}^2$ .

Find the net force on charge q.

A platinum wire has a resistance of $10\Omega$ at $0^{\circ }C$ and $20\Omega$ at ${273}^{\circ }C$. Find the value of temperature coefficient of platinum.

A wire of mass $5\text{kg}$ and length $3.5\text{m}$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is

Two metallic strips each of thickness ${10}^{-4}\text{m}$ are riveted together. Their coefficients of linear expansion are ${10}^{-5}{}^{\circ }{\text{C}}^{-1}$ and $2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1}$. If they are heated through a temperature change of $50{}^{\circ }\text{C}$, the bimetallic strip will bend to form an arc of radius

Moment of inertia of a body about a given axis is $1.5{\text{kg-m}}^2$. Initially the body is at rest. In order to produce a rotational kinetic energy of $1200\text{J}$, the angular acceleration of $20{\text{rad/s}}^2$ must be applied about the axis for a duration of

Given $\overrightarrow{F}=\left(x{y}^2\right)\hat{i}+\left(x^{2}y\right)\hat{j}N$. The work done by $\overrightarrow{F}$ when a particle is taken along the semicircular path OAB where the coordinates of B are (4,0) is

A boat of mass $M=100\text{kg}$ and length $L=20\text{m}$ is on a frictionless water surface. Two men $A$ of mass $m_1=25\text{kg}$ and $B$ of mass $m_2=50\text{kg}$ are standing at the two opposite ends. Now, both start travelling in opposite directions to each other and they reach the opposite positions of each other. Find the distance travelled by the $A$ w.r.t the ground.

A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are ${\gamma }_1$ and ${\gamma }_2$ respectively. If their temperature are increased by $\Delta T$ each, the fraction of the volume of metal submerged in mercury changes by a factor of

A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in figure. The thread goes over a fixed pulley and supports a weight to produce a tension. The lowest frequency with which the heavy string resonates is 120 Hz. If the movable support is pushed to the right by 10 cm so that the joint is placed on the pulley, what will be the minimum frequency at which the heavy string can resonate?

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass $=5.98\times {10}^{24}\text{kg}$) have to be compressed to be a black hole?

A particle executing SHM has maximum acceleration of $2\pi {\text{m/s}}^2$ and maximum velocity of $6\text{m/s}$. Find its time period

Find the direction of friction on A and B at the surfaces of contact between them (for the figure shown).

A body $A$ is thrown vertically upwards with such a velocity that it reaches a maximum height of $h$. Simultaneously, another body $B$ is dropped from height $h$. It strikes the ground and does not rebound. The relative velocity of $A$ wrt $B$ to time graph is best represented by : (upward direction is positive)

The potential energy of particle of mass 'm' is given by $U=\frac{1}{2}k{x}^2$ for x<0 and U = 0 for x $\ge$ 0. If total mechanical energy of the particle is E. Then its speed at $x=\sqrt{\frac{2E}{k}}$ is

Kinetic energy $\left(\text{in joule}\right)$ in one wave length of transverse wave is twice of its average kinetic energy per unit length The wave length of the transverse wave is

A cube floats in water with ${\left(\frac{1}{4}\right)}^{\text{th}}$ part outside the surface of water. If it floats in another liquid of relative density $\frac{4}{3}$ with $x^{th}$ part outside the liquid, then the value of $x$ is

The resultant of the two vectors having magnitude $2$ and $3$ is $1$. What will be their cross product?

How does the melting point of ice change with a change in atmospheric pressure?

On forgetting his 25th anniversary, Vijay as a present from his wife, receives a shoe of 0.5 kg thrown at him with 10 m/s velocity. Find the momentum of assault.

Two blocks $m_1$and $m_2$, are acted upon by the forces $F_1$ and $F_2$ as shown in the fig. If there is no relative sliding between the blocks and the ground is smooth, find the magnitude of static friction between the blocks.Make necessary assumptions.

The displacement (in $\text{m}$) equation of a particle is $x=3\text{sin}2t+4\text{cos}2t$. The amplitude (in $\text{m}$) and maximum velocity (in $\text{m/s}$) will be respectively.

A wave of frequency $680\text{Hz}$ has a wave velocity of $340\text{m/s}$ . Find the phase difference between two displacements of a certain point on the wave, whose time difference is $0.002\text{s}$.