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An Indian rubber cord $L\text{m}$ long and area of cross-section $A{\text{m}}^2$ is suspended vertically. Density of rubber is $D{\text{kg/m}}^3$ and Young's modulus of rubber is $E{\text{N/m}}^3.$ If the wire extends by $l\text{m}$ under its own weight, then extension $l$ is

In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. when this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction

Sir is there anything called centre of charge ? Like centre of mass.

Two trains each $50\text{m}$ long are moving parallel towards each other at speeds $10\text{m/s}$ and $15\text{m/s}$ respectively. At what time will they pass each other ?

Two slits in Young's experiment have widths in the ratio $1:25$. The ratio of intensity at the maxima and minima in the interference pattern, i.e. $\frac{I_{max}}{I_{min}}$ is

A cart of mass 'M' is at rest on a frictionless horizontal surface and a pendulum bob of mass 'm' hangs from the roof of the art. The string breaks, the bob falls on the floor, makes several collisions on the floor and finally lands up in a small slot made in the floor. The horizontal distance between the string and the slot is L. Find the displacement of the cart during the process ?

At time $t=0\text{s}$, a particle starts from rest at position $(4\text{m},8\text{m})$. It starts moving towards the positive $x$-axis with a constant acceleration of $2{\text{m/s}}^2$. After $2\text{s}$, it undergoes an additional acceleration of $4{\text{m/s}}^2$ in the positive $y$-direction. Find the coordinates of the particle (in $\text{m}$) after the next $5\text{s}$.

The angular momentum of electron in $n^{th}$ orbit is given by

A source of sound emits waves of frequency $f_0=1200\text{Hz}.$ The source is travelling with a velocity $v_1=30\text{m/s}.$ towards east. There is a large reflecting surface in front of the source which is travelling with a velocity $v_2=60\text{m/s}$ towards west. Speed of sound in air is $v=330\text{m/s}$. Find the ratio of wavelength $\left({\lambda }_1\right)$ of sound emitted by source when travelling towards the reflecting surface to the wavelength $\left({\lambda }_2\right)$ of sound approaching the source after getting reflected.

A person measures the time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration of g/3, the time period of the pendulum will be

A small mass slides down an inclined plane of inclination $\theta$ with the horizontal. The coefficient of friction is $\mu ={\mu }_{0}x$, where $x$ is the distance through which the mass slides down, and ${\mu }_0$ a constant. Then, the speed is maximum after the mass covers a distance of

A small magnet placed with is axis at ${30}^{\circ }$ with an external field of $0.06\text{T}$ experience a torques of $0.018\text{Nm}.$ The minimum work to rotate it from its stable to unstable equilibrium position is

If $V_e$ is the escape velocity and $V_0$ is the orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

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A magnetic needle of magnetic moment $6.7\times {10}^{-2}A{m}^2$ and moment of inertia $7.5\times {10}^{-6}kg{m}^2$ is performing simple harmonic oscillations in a magnetic field of $0.01T$. Time taken for $10$ complete oscillations is

At what distance eye 'E' will observe the fourth image (after four refractions from plane surfaces) of object 'O' from itself?

A small disc is set on rolling with speed $10\text{m/s}$ on the horizontal part of the track from right to left. There is curved part also as shown in the figure. To what height will the disc climb up on the curved path ? Assuming all track is rough and there is no slipping occur anywhere.