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Which of the following statement is incorrect regarding a thin lens?

A ring is rotating with an angular acceleration given by $\alpha =4t^3-\frac{3}{2}{t}^2$, where $t$ is time. Find the equation of angular speed $\omega$ if the ring starts from rest.

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नीचे दिए गए प्रश्न के लिए अनुच्छेद



When an object follows a circular path at constant speed, the motion is called uniform circular motion. When taking centre of circle at origin, the equation of circle is x² + y² = r², where r is radius of circle. The velocity of the object is continuously changing in direction and object undergoes acceleration.



In uniform circular motion, magnitude of acceleration towards centre of circle is $\left(\frac{v^2}{r}\right)$. Now answer the following question.



जब एक वस्तु नियत चाल से वृत्तीय पथ का अनुसरण करती है, तब गति को एकसमान वृत्तीय गति कहा जाता है। जब वृत्त के केन्द्र को मूल बिन्दु पर लिया जाता है, तब वृत्त की समीकरण x² + y² = r² है, जहाँ r वृत्त की त्रिज्या है। वस्तु के वेग की दिशा मे निरन्तर परिवर्तन हो रहा है तथा वस्तु त्वरित होती है।



एकसमान वृत्तीय गति में, वृत्त के केन्द्र की ओर त्वरण का परिमाण $\left(\frac{v^2}{r}\right)$ है। अब निम्नलिखित प्रश्न का उत्तर दीजिए।



Q. The acceleration (in m/s²) of the particle, when it is at point (5 m, 5 m) is



प्रश्न - जब कण बिंदु (5 m, 5 m) पर है, तब इसका त्वरण (m/s² में) है

When work is done on a body by an external force, its

Figure shows three forces applied to a trunk that moves leftward by $3$ m over a smooth floor. The force magnitudes are $F_1=5N,F_2=9N,$ and $F_3=3N$. The net work done on the trunk by the three forces

If the distances of an object and its virtual image from the focus of a convex lens of focal length f are 1 cm each, then f is

The time taken for a certain volume of gas to diffuse through a small hole was $2\text{min}$. Under similar conditions an equal volume of oxygen took $4\text{min}$ to pass. The molecular mass of the gas is:

A 60 kg man stands on a spring scale in the lift. At some instant he finds, scale reading has changed from 60 kg to 50 kg for a while and then comes back to the original mark. What should we conclude

The magnitude of the force (in $N$) acting on a body varies with time $t$ (in $\mu s$) as shown. $AB,BC$ and $CD$ are straight line segments. The magnitude of the total impule of the force on the body from $t=4\mu s$ to $t=16\mu s$ is

Tangential acceleration of a particle moving in a circle of radius $1\text{m}$ varies with time $t$ as shown in the figure (initial velocity of particle is zero). Time after which total acceleration of particle makes an angle of ${30}^{\circ }$ with radial acceleration is

Two particles A and B are moving with uniform velocity as shown in the figure given below at t = 0.

What is the shortest distance between two particles?

Find the excess pressure inside a mercury drop of radius 2.0 mm. The surface tension of mercury = 0.464 N/m

In the following arrangement, the system is initially at rest. The $5\text{kg}$ block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of blocks are

The coordinates of a moving particle at any time are given by $x=a{t}^2$ and $y=b{t}^2$. The speed of the particle at any moment is

A block of mass 0.1 kg is held against a wall applying a horizontal force of 5 N of the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is

A racer drives his bike starting from rest on a circular track of radius $40\text{m}$ and having tangential acceleration of $3{\text{m/s}}^2$. What is the magnitude of net acceleration of the racer $5\text{s}$ after he starts to drive the bike?

Find the derivative of $y\left(x\right)=\frac{x^3}{(x+1{)}^2}$ with respect to $x$.

How can a string of length $l$ be made into a rectangle so as to maximize the area of the rectangle?

An automobile moves on a road with a speed of $54\text{km/hr}$. The radius of its wheels is $0.45\text{m}$ and the moment of inertia of the wheel about its axis of rotation is $3{\text{kg-m}}^2$. If the vehicle is brought to rest in $15\text{s}$, the magnitude of average torque transmitted by its brakes to the wheel is

The de-Broglie wavelength of a neutron at ${27}^{\circ }C$ is $\lambda$ . What will be its wavelength at ${927}^{\circ }C$

Two blocks are in contact on a frictionless table one has a mass m and the other 2 m as shown in figure. Force F is applied on mass 2m then system moves towards right. Now the same force F is applied on m. The ratio of force of contact between the two blocks will be in the two cases respectively.

The curve between $v_{rms}^2$ and pressure $P$ for constant volume is

Two masses of 1g and 9g are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is

A force acts on a $3\text{gm}$ particle in such a way that the position of the particle as a function of time is given by $x=3t-4t^2+t^3,$ where $x$ is in metres and $t$ is in seconds. The work done during the first $4$ second is

If sides of a rectangle with given perimeter are $a$ & $b$, then find the relation between $a$ & $b$ for which area of the given rectangle is maximum.

Find the capacitance between P and O. Each capacitor has capacitance $C$

A ball moving with velocity $2{\text{ms}}^{-1}$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in ${\text{ms}}^{-1}$) after collision will be

Electric field in the given region is vertically downwards. An open hemisphere of radius $a$ is placed as shown. Find the net flux of electric field through the curved surface of hemisphere.

Two resistors are connected in series across a $5\text{V rms}$ source of alternating potential. The potential difference across $6\Omega$ resistor is $3\text{V}$. If R is replaced by a pure inductor $L$ of such magnitude that current remains same, then the potential difference across $L$ is

A small block of mass $m=2kg$ is projected on a larger block of $20kg$ and of length $20\text{metres}$, with a velocity of $vm/s$ as shown in the figure. The coefficient of friction between the two blocks is $1.2$, while between the lower block and ground is $0.1$. The time taken by the small block to fall off the larger block is (Take $g=10m/s^2$)

If a body travels a distance of $97.52\text{m}$ along a straight line in $2.54\text{s}$, then its speed in appropriate significant figures is

Angle of minimum deviation is equal to the angle of prism A of an equilateral glass prism. The angle of incidence at which minimum deviation will be obtained is

A particle executes simple harmonic motion between x = -A and x = +A. The time taken for it to go from 0 to A/2 is $T_1$ and to go from A/2 to A is $T_2.$ Then

Two blocks of masses $2\text{kg}$ and $4\text{kg}$ are arranged as shown in figure. Then, find the maximum value of force $F$, for which both blocks will move together.

A simple harmonic wave of amplitude 2 units is travelling along x - axis. At a given instant, displacements for two different particles on the wave are 1 unit and $\sqrt{2}$ units. If the wavelength of the wave is $\lambda$, find the distance between them.

The work functions for sodium and copper are 2eV and 4eV. Which of them is suitable for a photocell with $4000\stackrel{\circ }{A}$ light

A straight line makes an angle $60°$ with the positive x- axis then its slope is

A body travels for $15\text{sec}$ starting from rest with constant acceleration. If it travels distances $S_1,S_2$ and $S_3$ in the first five seconds, second five seconds and next five seconds respectively the relation between $S_1,S_2$ and $S_3$ is

The trajectory of a projectile in a vertical plane is: $y=ax-b{x}^2$,

where $a$ and $b$ are constants and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The maximum height attained is

Position vector of a particle moving in $x-y$ plane at time $t$ is $\overrightarrow{r}=a(1-\cos \omega t)\hat{i}+a\sin \omega t\hat{j}$ and the angular velocity of the particle is ${\omega }_o\hat{k}$. The magnitude of the linear velocity of particle at $t=\frac{\pi }{2\omega }$ is

An organ pipe $P_1$ closed at one end is vibrating in its first overtone and another organ pipe $P_2$ opened at both ends is vibrating in its third overtone are in resonance with a given tuning fork. The ratio of length of organ pipe $P_1$ and $P_2$ is

In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to $n^{th}$ mass is

A particle of mass $2\text{kg}$ initially at origin $(0,0)$ moves with an initial velocity $\overrightarrow{V}=4\hat{i}+4\hat{j}\text{m/s}$. If a constant force $\overrightarrow{F}=-20\hat{j}\text{N}$ is applied on the particle, the $x-$coordinate of the particle when its $y-$coordinate again becomes zero is

Two equal spheres of mass $m$ are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and is reduced to rest. Find the loss of K.E

Transverse waves travel with a speed of $40\text{m/s}$ in a string under a tension of $12\text{N}$. What tension is required for a wave speed of $60\text{m/s}$ in the same string?

A block is gently placed on a conveyor belt moving horizontally at a constant speed. After $t=4\text{s}$, the velocity of the block becomes equal to the velocity of the belt. If the coefficient of static friction between the block and the belt is $\mu =0.2$, then what is the velocity of the conveyor belt ?