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The belt of an electrostatic generator is $50cm$ wide and travels $30cm/s$. The belt carries charge into the sphere at a rate corresponding to ${10}^{-4}A$. What is the surface density of charge on the belt?

Two identical uniform discs roll without slipping on two different surfaces $AB$ and $CD$ starting at $A$ and $C$ with linear speed $v_1$ and $v_2$, respectively, and always remain in contact with the surfaces. If they reach $B$ and $D$ with the same linear speed and $v_1=3m/s$ then $v_2$ in $m/s$ is $(g=10m/s^2)$

The wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen atom spectrum is __________ nm

A block $A$ of mass $m_1$ and block $B$ of mass $m_2$ are connected together by a spring and placed on a bearing surface as shown. The block $A$ performs free vertical harmonic oscillations with amplitude $A_{max}$ and frequency $\omega$. Assuming that block $B$ doesn't leave the surface and neglecting the mass of the spring, find the maximum and minimum value of force ($R_{max}\&R_{min}$) that the system exerts on the bearing surface.

What is the centripetal force acting on a car of weight $15000\text{N}$ moving on a frictionless road banked at an angle of ${30}^{\circ }$?

A player with 3 m long iron rod is running towards east with a speed of 30 km/hr. Horizontal component of earth's magnetic field is $4$ x ${10}^{-5}Wb/m^2$. If he is running with rod in horizontal and vertical positions, then the potential difference induced across the ends of the rod in each of the cases would be

A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x = 0. It begins with a displacement y = 0, at t = 0, according to equation $y=0.2sin(kx\pm \omega t)$. How much time passes between the first two instant when this particle has a displacement of y = 0.1 m?

An ac source of variable frequency $f$ is connected to an $LCR$ series circuit. Which one of the graphs in figure represents the variation of current $I$ in the circuit with frequency $f$ ?

A ball is kept at a height h above the surface of a heavy transparent sphere made of a material of refractive index $\mu$. The radius of the sphere is R. At t = 0, the ball is dropped to fall normally on the sphere. Find the speed of the image funned as a function of time for $t<\sqrt{\frac{2h}{g}}$. Consider only tbe image by a single refraction.

A rectangular film of liquid is extended from $(4cm\times 2cm)$ to $(5cm\times 4cm)$. If the work done is $3\times {10}^{-4}J$, the value of the surface tension of the liquid is

What is the equation of a sinusoidal wave moving in the positive x direction with wave length 6 m and time period 0.5s. The amplitude of the wave is 5 m.

Compressibility factor $\left(Z\right)$ for $N_2$ at $-{23}^{\circ }\text{C}$ and $821\text{atm}$ is $1.25$. Calculate the number of moles of nitrogen gas needed to fill a gas cylinder of $100\text{litre}$ capacity under given condition.

The equation of motion of a particle of mass $1\text{g}$ is $\frac{d^{2}x}{d{t}^2}+{\pi }^{2}x=0$, where $x$ is displacement (in $\text{m}$) from mean position. The frequency (in $\text{Hz}$) of oscillation is

A long horizontally fixed wire carries a current of 100A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N m^-1 . What should be the separation between the two wires so that the upper wire is just supported by magnetic repulsion?

If $y=\sin \left(\ln x\right)$, then $\frac{dy}{dx}$ will be

A car starts from rest and accelerates uniformly to a speed of $90\text{km/h}$ in $5\text{s}$. The distance covered by the car in this time interval is

If the length of a cylinder is measured to be $4.28\text{cm}$ with an error of $0.01\text{cm}$, then the percentage error in the measurement will be

Two identical tuning forks vibrating at the same frequency 256 Hz are kept fixed at some distance apart. A listener runs between the forks at a speed of 3.0 m/s so that he approaches one tuning fork while receding from the other (figure). Find the beat frequency observed by the listener. Speed of sound in air = 332 m/s.

The angular speed of a body changes from ${\omega }_1$ to ${\omega }_2$ due to changes in its moment of inertia without applying torque. The ratio of radius of gyration in the two cases is

A body is projected with an initial velocity of $20\hat{i}+20\hat{j}$. It clears a wall at a distance of 20 m. Find the velocity when it clears the wall.

Water stands at level A in the arrangement shown in the figure. What will happen if a jet of air is blown into the horizontal tube ?

The figure shows two points source which emit light of wavelength $\lambda$ in phase with each other and are at a distance d = 5.5$\lambda$ apart along a line which is perpendicular to a large screen at a distance L from the centre of the source. Assume that d is much less than L. Which of the following statement is (are) correct?

A wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross - sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$ and its Young's modulus is $Y$, the force that one part of the wheel applies on the other part is-

Two gas bulbs A and B are connected by a tube having a stopcock. Bulb A has a volume of 100 mL and contains hydrogen. After opening the gas moves from A to the evacuated bulb B, the pressure falls down to 40%. The volume (mL) of B must be:

Four bodies of masses $2\text{kg},3\text{kg},5\text{kg}$ and $8\text{kg}$ respectively are placed at the four corners of a square of side $2\text{m}$. Then, position of centre of mass of the system will be:

A man is pulling a block resting on the ground by applying force $F=(20t+40)\text{N}$ as shown in the figure. If the pulley is frictionless and mass of the block is $4\text{kg}$, find out the power delivered by the force, $3\text{seconds}$ after the man starts pulling the block. (Take $g=10{\text{m/s}}^2$)

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of

A particle executing SHM while moving from one extremity is found to be at distances $x_1,x_{2}and{x}_3$ from the mean position at the end of three successive seconds. The time period of oscillation is ($\theta$ used in the following choices is given by $cos\theta =\frac{x_1+x_3}{2x_2}$

A plane mirror is inclined at an angle of ${45}^{\circ }$ with the horizontal and having one of its end at the origin(O) as shown in figure. An object is kept at $x=-2\text{cm}$. The position coordinates of the image of $P$ will be

Where should the tank be punctured so that water coming out has maximum horizontal range?

A cell of emf E having an internal resistance r is connected to an external resistance R. The potential difference V across the resistance R varies with R as shown by the curve:

A capacitor has rectangular plates of length a and width b. The top plate is inclined at a small angle as shown in the figure. The plate separation varies from $d=y_0$ at the left to d $=2y_0$ at the right where $y_0$ is much less than a or b. What is capacitance of the system?

A granite rod of $60cm$ length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7\times {10}^{3}kg/m^3$ and its Young's modulus is $9.27\times {10}^{10}Pa$. What will be the fundamental frequency of the longitudinal vibrations?

Two boys are standing at the ends $A$ and $B$ of a ground, where $AB=a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously along a straight line with velocity $v$ and catches the other boy in a time $t$, where t is

Find the moment of inertia of ring of mass $M$ and radius $R$ about the axis passing through the ring diametrically. If moment of inertia about the axis passing through its center of mass and perpendicular to the plane is $M{R}^2$.

Two particles A and B initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of A is $v$ and that of B is $2v$, the velocity of the center of mass of the system will be

If pressure at half depth of a lake is equal to $\frac{2}{3}rd$ pressure at the bottom of the lake, then what is the depth of the lake?
(Take atmospheric pressure as ${10}^5\text{Pa}$, density of water as $1000{\text{kg/m}}^3$ and $g=10{\text{m/s}}^2$)

When 40 kV is applied across an X-ray tube, X-ray is obtained with a maximum frequency of 9.7 $\times {10}^{18}$ Hz. Calculate the value of Planck constant from these data.

The magnitude of the displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as

The uncertainty in the velocity of a cricket ball of mass $100\text{g}$, when uncertainty in its position is of the order of $1\stackrel{o}{A}$, would be :

What do we mean when we say we completely understand mechanics?

A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are 60 V and $40\text{V}$ respectively.
The value of inductance L is

Two boys having masses $m_1=4\text{kg}$ and $m_2=2\text{kg}$ are seating on a seesaw of length $r=1\text{m}$ as shown in figure. Find the net torque due to weight of boys, acting about the midpoint $O$.
(Take $g=10{\text{m/s}}^2$ and anti-clock wise rotation as $+ve$)