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A person of mass $60kg$ inside a lift of mass $940kg$ presses the button on control panel. The lift starts moving upwards with an acceleration of 1 $m/s^2$. If $g=10m/s^2$ , the tension in the supporting cable is

A turn of radius $20\text{m}$ is banked for vehicles going at a speed of $36\text{km/h}$. If the coefficient of friction between the road and the tyres is $0.4$, what are the possible speeds of a vehicle so that it neither slips down nor skids up ?

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the y-axis in the y-z plane at $z=\frac{\sqrt{3}}{2}a$. If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is $\frac{\lambda L}{n{\epsilon }_0}$ (${\epsilon }_0=$ permittivity of free space), then the value of $n$ is

Two particles of charges Q₁ and Q₂ placed at a some distance the force between them is f if the distance between them is reduced to half and charge on each particle is doubled the force between the particles would become?

Two circular coils $\text{A}$ and $\text{B}$ of radii $a$ and $b$ respectively $(\text{with}b>>a)$ have their planes perpendicular to the plane of the page. They are separated co-axially by a distance $x=\sqrt{3}b$ as shown in the figure. A transient current $I$ flows through coil $\text{B}$ for a very short time interval. If the resistance of coil $\text{A}$ is $R$, then the charge that flows through coil $\text{A}$ during the short time interval will be

Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are connected by a massless string as shown in figure. A vertical force $F$ is applied on the $5\text{kg}$ block. Find the value of $F$ if tension in the string is $40\text{N}$. $(g=10{\text{m/s}}^2)$

If we multiply force by displacement along force, we get ____.

A line makes angles $\alpha ,\beta$ and $\gamma$ with the coordinate axes. If $\alpha +\beta ={90}^{\circ },$ then $\gamma =$

A long solenoid has $1000$ turns per unit length, radius $0.5\text{m}$ and carries a current $2\text{A}$ is kept in gravity free region. From its axis at a distance $0.2\text{m}$, an electron is placed. If the current in the solenoid is suddenly switched off, find the velocity attained by the electron.

A wire carrying current $l$ is bent in the shape $ABCDEFA$ as shown, where rectangle $ABCDA$ and $ADEFA$ are perpendicular to each other. If the sides of the rectangles are of length $a$ and $b$, then the magnitude and direction of magnetic moment of the loop $ABCDEFA$ is

Calculate the force between two masses of $50kg$ and $100kg$ separated by a distance of $10m.$

A single phase transformer is rated as 3 kVA, 400/230 V, 50 Hz. Open circuit test is conducted by placing instruments at LV side. Open circuit test readings are

$V_{OC}=230V$, $I_{OC}=1.3A$, $P_{OC}=100W$

The resistance and reactance of exciting branch referred to high voltage side are respectively

An L-C-R circuit is equivalent to a damped pendulum. In an L-C-R circuit, the capacitor is charged to $Q_0$ and then connected to $L$ and $R$ as shown. If a student plots graphs of the square of maximum charge $\left(Q_{Max}^2\right)$ on capacitor with time ($t$) for two different values $L_{1}and{L}_2(L_1>L_2)$ of $L$, then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale)

An elastic circular wire of length l carries a current I. It is placed in a uniform magnetic field $\overrightarrow{B}$ (Out of paper) such that its plane is perpendicular to the direction of $\overrightarrow{B}$. The wire will experience

A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of $2\text{m/s}$. At what angle $\alpha$ with the vertical should the wind screen be placed so that rain drops falling vertically downwards with velocity $6\text{m/s}$ strike the wind screen perpendicularly?

Vector $\overrightarrow{A}$ of magnitude 4 units is directed along the positive x-axis. Another vector $\overrightarrow{B}$ of magnitude 3 units lies in the x-y plane and makes an angle ${30}^{\circ }$ with the positive x-axis as shown in the figure. Then $\overrightarrow{A}.\overrightarrow{B}$ is

A stone tied to a string is rotated with a uniform speed in a vertical plane. If mass of the stone is $m$, the length of the string is $r$ and the linear speed of the stone is $v$, when the stone is at its lowest point, then the tension in the string will be ($g=$ acceleration due to gravity)

The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used

[DPMT 1995]

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A $600\text{Hz}$ source, an observer and the wind are moving as shown in the figure with respect to the ground. Find the frequency heard by the observer. Take sound speed in stationary air to be $330\text{m/s}$.

A mass m supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration with the mass fall on release?

A wave pulse is generated in a string that lies along x-axis. At the points A and B, as shown in figure, if $R_{A}and{R}_B$ are ratios of magnitudes of particle speed to the wave speed, then

A Force $F$ making an angle ${60}^{\circ }$ with the horizontal, acts on an object and displaces it by $0.4\text{m}$ along the horizontal direction. If the work done by the force is $1\text{Joule}$, then the force $F$ is

The fraction of volume occupied by the nucleus with respect to the total volume of an atom is

Figure shows a block of mass $m$ placed on a horizontal surface. The coefficient of static friction between the block and the surface is $\mu$. The maximum force $F$ that can be applied at point $O$ such that the block does not slip on the surface is

A body of mass $2kg$ has an initial speed of $5m/s$. A force acts on it for some time in the direction of motion. The force-time graph is shown in the figure. The final speed of the body is

The equation of the plane which passes through the point of intersection of lines $\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ and at greatest distance from origin is

A uniform metre stick of mass $250\text{gm}$ is suspended from the ceiling through two vertical strings of equal lengths. A small object of mass $50\text{gm}$ is placed on the stick at a distance of $70\text{cm}$ from the left end. Find the tension in both the strings. Take $g=10{\text{m/s}}^2$.