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Mr. $A,B\text{and}C$ are trying to put a heavy piston into a cylinder at a mechanical workshop in a railway yard. If they apply forces $F_1,F_2\text{and}{F}_3$ respectively on the ropes, then, what is the relation between the forces if piston decends vertically with uniform speed?

A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.

A car is travelling along a circular curve that has a radius of $50\text{m}$ with a constant tangential acceleration. If the speed of the car changes from $36\text{km/hr}$ to $45\text{km/hr}$ in $5\text{seconds}$, the angular acceleration of the car is.(No slipping between road and car tyre)

If $N_0$ is the original mass of the substance of half-life period $t_{1/2}=5$ years, then the amount of substance left after 15 years is

Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is :

The path of photoelectrons emitted due to electromagnetic radiation incident on a sample of material A, is found to have a maximum bending radius of 0.1m in a magnetic field of $\left(\frac{\sqrt{2}}{3}\right)\times {10}^{-4}T.$ When the radiation is incident normally on a double slit having a slit separation of 0.1 mm, it is observed that there are 10 fringes in a width of 3.1 cm on a screen placed at a distance of 1m from the double slit. Find the work function (eV) of metal [Given $hC=12400eV-A^{\circ }]$___

Three rings each of mass m and radius r are placed in a plane touching each other as shown. The radius of gyration of the system about the axis as shown in the figure is

A ball is projected from point A with a velocity 10 $m{s}^{-1}$ perpendicular to the plane as given. The range of the ball on plane is( in m),+

The springs in fig. $A$ and $B$ are identical but the length of spring $A$ is three times the length of each spring in $B$. The ratio of period $T_A/T_B$ is

A body covers $10m$ in $2^{nd}$ second and $25m$ in $5^{th}$ second of its motion. If the motion is uniformly accelerated, how far will it go in the $7^{th}$ second?

Time is measured using petioper motion.describe.

A particle of mass $5\text{kg}$ is dropped from a tower of height $10\text{m}$. Find the difference of work done by gravity from point $A$ to $B$ $\left(W_{AB}\right)$ and change in potential energy from $A$ to $B$ $\left(U_{AB}\right)$.

Does resitivity play any role in case of ideal and real battery?

Explain -

Dimensional quantities

Ddimensionless quantities

A body of mass $500\text{g}$ is moving in a circular path of radius $\frac{10}{{\pi }^2}\text{cm}$ with an angular speed of $2\pi \text{rad/s}$. The centripetal force is

Who proposed charge and how we can say charge is positive or negative or neutral and what theorem are used ? Why and give reason?

In an isothermal expansion

A satellite is revolving round the earth with orbital speed $v_0$. If it stops suddenly, the speed with which it will strike the surface of earth would be

($v_e$= escape velocity of a particle on earth's surface)

From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle to hit the ground is $n$ times that taken by it to reach the highest point of its path. The relation between $H,u$ and $n$ is

A block of mass $m$ lying on a smooth horizontal surface is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is

#What is plastic deformation

#What is ductile material

#What is brittle matarial

A stone tied to a string of length $l$ is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest point and has a speed $u$. The magnitude of change in velocity as it reaches its highest point of the circle is

Work done in carrying 2 C charge in a circular path of radius 2 m around a charge of 10 C is

A swimmer appears to be moving perpendicular to a man going upstream in a boat. If the velocity of boat w.r.t water is 3 m/s and velocity of river is 1 m/s. Find velocity of swimmer w.r.t ground if it takes 20 seconds for him to cross 60 metre wide river.

The position $x$ of a particle having mass $m$ moving along $x$ - axis at time $t$ is given by the equation $t=\sqrt{x}+2$, where $x$ is in $\text{m}$ and $t$ in $\text{s}$. Find the work done by the force in first $4\text{s}$.

Find out the value of current through 2$\Omega$ resistor in the following circuit

A small disc of mass $m$ is placed on a body of mass $M$ at rest. If the disc is set in horizontal motion with velocity $v$ as shown,

(Assume that disc leaves from surface of $M$ vertically at A and all surfaces are smooth)
Find velocity of mass $M,$ when disc leaves the surface of $M.$

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4$\mu$F capacitors), at a point distant 30m from it, would equal:

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

The velocity of the particle is given by $v=3t^2+2t$ in $\text{m/s}$. The acceleration and displacement of the particle as a function of time respectively are

The acceleration of a particle which moves along the positive x-axis varies with its position as shown. The velocity of the particle is $0.8m/s$ at $x=0$ and the acceleration becomes zero after $x=1.4m$. The maximum velocity of the particle (in m/s) is

A sound wave travels a distance $l$ in helium gas in time $t$ at a particular temperature. If at the same temperature a sound wave is propagated in oxygen gas, it will cover the same distance $l$ in time (approximately)

Considering an ideal refrigerator, heat from its inside at a temperature of $277\text{K}$ is transferred to a room at temperature of $300\text{K}$. Find the amount of heat extracted for each Joule of electrical energy consumed by refrigerator.

In an orbital motion, the angular momentum vector is :

Find the acceleration of the $3m$ block when the system is released from rest. All other surfaces are smooth except between $m$ and $2m$. Take $g=10m/s^2$

A force $F$ acting on a particle varies with position $x$ as shown in figure. The workdone by this force in displacing the particle from $x=-1\text{m}$ to $1\text{m}$.

A light string is tied to another light string of equal length $L$ and two strings are tied to the fixed supports at their other ends. The strings are set into vibration so that junction $A$ is a node. The wavelength of the loops formed to the left and to the right of the junction point $A$ is ${\lambda }_1$ and ${\lambda }_2$ respectively. Find the difference of the number of the loops formed to the right and to the left of the point $A$.

Two straight and long conductors AOB and COD are perpendicular to each other and carry currents of $I_{1}and{I}_2$. The magnitude of the magnetic field at a point P at a distance a from point 0 in a direction perpendicular to the plane ABCD is

A ball is thrown vertically upward from the top of a cliff. Take the starting position of motion as origin and upward direction as positive. Column I specifies the position, velocity and /or acceleration of the particle at any instant. Column II given their signs $(+)$ or $(-)$ at that moment. Match the columns
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i.When the ball is above the point}& \text{a. always positive}\\ \text{of projection, its displacement is}& \\ \text{ii. When the ball is above the point}& \text{b. always negative}\\ \text{of projection, its velocity is}& \\ \text{iii. When the ball is above the point}& \text{c. May be positive or may be}\\ \text{of projection, its acceleration is}& \text{negative}\\ \text{iv.When the ball is below the point}& \text{d. may be zero}\\ \text{of projection, its acceleration is}& \end{array}$

A vertical mass-spring system executes simple harmonic oscillations with a period of 2 s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is

Two speakers are separated by a distance of $3\text{m}$. A person stands at a distance of $4\text{m}$, directly in front of one of the speakers. If $n$ stands for any integer, find the frequencies (in audible range) for which the listener will hear a minimum sound intensity. Speed of sound in air is $320\text{m/s}$.

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as, $a_c=k^{2}r{t}^2$ , The power delivered to the particle by the forces acting on it is