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A stone of mass 2kg is tied to a string of length 0.5m. If the breaking tension of the string is 900N, then the maximum angular velocity, the stone can have in uniform circular motion is:

A simple telescope consisting of an objective lens of focal length 30 cm and that of its eye-lens is 3 cm. It is focused on a scale 2 metres distant from it. The distance of objective lens from eye-lens to see with relaxed eye is

Two identical small spheres A and B lie on a smooth horizontal circular groove at opposite ends of diameter. A is projected along the groove and it hits B at time t. If e is the coefficient of restitution, then the second impact will occur after the time.

An electrostatic field line is a continous curve. That is, a field line cannot have sudden breaks. Why not?

Explain why two field lines never cross each other at any point?

The distance between a convex lens and a plane mirror is $40cm$. The parallel rays incident on the convex lens after reflection from the mirror form image at the optical centre of the lens. Focal length of the lens will be

The variation of density of water with temperature is represented by

A string of length $1.5\text{m}$ with both its ends clamped is vibrating in fundamental mode. Amplitude at the centre of string is $4\text{mm}$. What is the minimum distance between two points having amplitude $2\text{mm}$?

What is the period of a pendulum formed by pivoting a meter stick so that it is free to rotate about a horizontal axis passing through the $75\text{cm}$ mark?

Which of the given statement(s) about N, O, P and Q with respect to M is / are correct?

A person living in Shimla observed that cooking food without using pressure cooker takes more time. The reason for this observation is that at high altitude

(a) pressure increases (b) temperature decreases

(c) pressure decreases (d) temperature increases

Charge are placed on the vertices of a square as shown. Let $\overrightarrow{E}$ be the electric field and V and potential at the center. If the charges on A and B are interchanged with those on D and C respectively, then

A particle moves along the positive x-axis from origin with velocity, $V_0$ = 2m/s and a = 6(t - 1) where't' is in seconds. Which of these graphs are correct?

Figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?

If the horizontal range is four times the maximum height attained by a projectile then the angle of projection is

The process of superimposing signal frequency (i.e. audio wave) on the carrier

wave is known as [AIIMS 1987]

A particle executing SHM oscillates between two fixed points separated by $20\text{cm}$. If its maximum velocity is $30\text{cm/s}$, find its velocity when the displacement is $5\text{cm}$ from the mean position.

A body cools from 3T to 2T in 5 minutes. In these 5 minutes, energy emitted by the body decreases by

A boat which has a speed of 5 km/h in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/h is:

Thermal conductivity of the conductor shown in the figure is $0.92{\text{cal/cm s}}^{\circ }\text{C}$. Find the thermal resistance between points $P$ and $Q$ (in ${\text{s}}^{\circ }\text{C/cal}$).

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lift's motion is given in Column I and the distance where the water jet hits the floor of the lift is given in Column II. Match the statements from Column I with those in Column II and select the correct option using the code given below the lists.
$\begin{array}{cc}\text{Column~I}& \text{Column~II}\\ \text{(A) Lift is accelerating}& \text{1. d = 1.2 m}\\ \text{vertically up.}& \\ \text{(B) Lift is accelerating}& \text{2. d > 1.2 m}\\ \text{vertically down with}& \\ \text{an acceleration less}& \\ \text{than the gravitational}& \\ \text{acceleration.}& \\ \text{(C) Lift is moving}& \text{3. d < 1.2 m}\\ \text{vertically up with}& \\ \text{constant speed}.& \\ \text{(D) Lift is falling freely.}& \text{(4) No water leaks out of the jar}\end{array}$

A small block of mass $m$ rests on a smooth wedge of angle $\theta$. With what horizontal acceleration $a$ should the wedge be pulled $($as shown in the figure$)$ so that the small block falls freely?

Figure shows two blocks in contact and sliding down the inclined surface of inclination ${30}^{\circ }$. Coefficient of friction between the block of mass $4\text{kg}$ and the inclined plane is ${\mu }_1=0.3$ and that between the block of mass $2\text{kg}$ and the inclined plane is ${\mu }_2=0.20$. Assume coefficients of static and kinetic friction to be equal. Find the acceleration of $2\text{kg}$ block. Take $g=10{\text{m/s}}^2$.

A particle of mass $m$ is attached to a spring of natural length $L$ and spring constant $k$. If it is rotated in a horizontal plane with an angular speed $\omega$, then what will be the new length of the spring ?

A thin wire of uniform density is bend in the form of an arc of a circle which subtends an angle $\alpha$ at the centre of the circle as shown in the figure. Where is the centre of mass of this circular arc located?

The intensity of radiation emitted by the sun has its maximum value at a wavelength $510\text{nm}$ and that emitted by another star has the maximum value at $350\text{nm}$. If we treat them as black bodies, then the ratio of the surface temperature of the sun and the star is

An ideal gas is taken along the process $AB$ as shown in the $P-V$ diagram. Find the volume of the gas where the temperature becomes maximum.

A truck driver drives $20\text{km}$ down the road in $5\text{minutes}$ . He then reverses and drive $12\text{km}$ back down the road in $3\text{minutes}$. What is the average velocity?

The gravitational force acting on a particle of 1 g due to a similar particle is equal to $6.67\times {10}^{-17}N.$ Calculate the separation between the particles.

A uniform homogenous rope of mass ${}^{\prime }{m}^{\prime }$ and length ${}^{\prime }{l}^{\prime }$ is pulled by a force $F$ on a smooth inclined plane of angle $\theta$. Find the force on the rope at a distance $x$ from the end where force is applied.

A rod of length $l=10\pi \text{m}$ is rotating about a perpendicular bisector passing through its C.O.M and having moment of inertia, ${\pi }^2{\text{kg-m}}^2$. If same rod is bent into semi circular arc of radius $r$ as shown in figure and rotated about the same axis in same plane, then moment of inertia of arc will be

If the speed of a car is given as $v=2t+2\text{m/s}$, the average speed in $10sec$ is

Indicator diagram of an ideal gas is as shown in figure. Find the workdone by the gas in the process $ABCD$.

What is Tensile strength ?

A block of mass 2.0 kg kept at rest on an inclined place of inclination ${37}^{\circ }$ is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for on second. (a) Show that the work done by the applied force does not exceed 40 J. (b) Find the work done by the force of gravity in that one second if the work done by the applied force is 40 J.(c) Find the kinetic energy of the block at the instant the force ceases to act. Take g=$10m/s^2$.

A pump is required to lift $800\text{kg}$ of water per minute from a $10\text{m}$ deep well and eject it with speed of $20\text{m/s}$. The power required (in watts) of the pump will be
(Take $g=10m/s^2$)

Three particles of masses $300g,800g$ and $700g$ are placed at positions $A(2,4),B(3,5)$ and $C(-3,-1)$ respectively. What is the moment of inertia of the system about the origin?

If a magnetic material is having magnetic susceptibility (x) = -1 , then the relative magnetic permeability and type of magnetic material is ??

If $\gamma$ be the ratio of molar heat capacity of an ideal gas, then degree of freedom for the molecule of gas is

How much work would be done by the electric field if Q = 20 C were

moved from A (8 V) to B (3.5 V)?

A book is lying on the table. What is the angle between the action of the book on the table and reaction of table on the book?