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The kinetic energy $K$ of a particle moving along a circle of radius $R$ depends on the distance covered as $K=a{s}^2,$ where $\alpha$ is a constant. The force acting on the particle is

What strength does a fishing line needs to stop a $10kg$ salmon (fish) swimming at $9m/s$ in a distance of $4.5m$ ? (Assume deceleration of salmon due to fishing line is constant)

An artificial satellite of earth is launched in circular orbit in equatorial plane of the earth and satellite is moving from west to east. With respect to a person on the equator, the satellite is completing one round trip in $24\text{hours}$. Mass of earth is, $M=6\times {10}^{24}\text{kg}$. For this situation, orbital radius of the satellite is (Take $G=6.67\times$${10}^{-11}{\text{Nkg}}^{-2}{\text{m}}^2$)

A uniform rod of length $l$ & mass $M$ is free to rotate about frictionless pin through one end. The rod is released from rest in a horizontal position. Find momentum of system (rod) when rod is at its lowest position.

An oscillator is nothing but an amplifier with ____________.

A p-type semiconductor has acceptor level of $57\text{meV}$ above the valence band. Find the maximum wavelength of light which can create a hole

Two parallel rays are travelling in a medium of refractive index ${\mu }_1=\frac{4}{3}$. One of the rays passes through a parallel glass slab of thickness $t$ and refractive index ${\mu }_2=\frac{3}{2}$. The path difference between the two rays due to the glass slab will be

The bob of a $0.2\text{m}$ pendulum describes an arc of circle in a vertical plane. If the tension in the cord is $\sqrt{3}$ times the weight of the bob when the cord makes an angle ${30}^{\circ }$ with the vertical, the magnitude of acceleration of bob in that position will be:

The overall closed loop transfer function $\frac{C\left(s\right)}{R\left(s\right)}$ represented in the figure, will be

A small circular loop of conducting wire has radius $a$ and carries current $i$. It is placed in a uniform magnetic filed $B$ perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period $T$. If the mass of the loop is $m$ then:

The length of the compound microscope is $18\text{cm}$. Its magnifying power, for the relaxed eye, is $28$. Find the object distance from the objective lens if the focal length of the eyepiece is $4\text{cm}$.

A ball of mass 0.4 kg moving with uniform speed of $2m{s}^{-1}$ strikes normally a wall and rebounds. Assuming the collision to be elastic and the time of contact of the ball with the wall as 0.4s, find the force exerted on the ball

The resolving power of an electron micrsoscope operated at 16 $kV$ is $R$. The resolving power of the electron microscope when operated at $4kV$ is

A uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height $a(a<R)$ by applying a force $F$ at its centre $O$ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of $F$ required is :

The mean square speed of the molecules of a gas at absolute temperature T is proportional to

An object moves velocity $\overrightarrow{v}$ having constant accelaration $\overrightarrow{a}$. Which of the following expressions are variable quantities ?

A mass $m$ is revolving in a vertical circle at the end of a string of length $20\text{cms}$. By how much does the tension of the string at the lowest point exceed the tension at the topmost point

Source and observer both start moving simultaneously from origin one along $\text{X-axis}$ and the other along $\text{Y-axis}$ with speed of source = $2$$($speed of observer$)$. The graph between the apparent frequency $\left(f\right)$ and time $\left(t\right)$ observed by observer would be

$($Here, $f_0=$ natural frequency of source$)$

When any natural calamity happens does the internal energy of universe gets affected?If so does it violate first law of thermodynamics that internal energy of universe is always constant.

Five charges of each $+q$ are placed of the five corners of a regular hexagon. The resulant electric field at the centre is $E$. If the charges in the $1^{st}$ and $2^{nd}$ corner are removed, then the resultant electric field at the centre is

The natural frequency (rad/sec) of the system shown in figure. below is.

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved

Under steady state, the temperature of a body

A metal sphere $\text{A}$ of radius $r_1$ charged to a potential ${\varphi }_1$ is enveloped by a thin walled conducting spherical shell $\text{B}$ of radius $r_2$. Then potential ${\varphi }_2$ of the sphere $\text{A}$ after it is connected to the shell $\text{B}$ by a thin conducting wire will be:

In the figure below, $P$ and $Q$ are two equally intense coherent sources emitting radiation of wavelength $20\text{m}$. The separation between $P$ and $Q$ is $5\text{m}$ and the phase of $P$ is ahead of that of $Q$ by ${90}^{\circ }.A,B$ and $C$ are three distinct points of observation, each equidistant from the midpoint of $PQ.$ The intensities of radiation at $A,B,C$ will be in the proportion,

In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slit. It is found that the $9^{th}$ bright fringe is at a distance of 7.5 mm from the second dark fringe from the centre of the fringe pattern. The wavelength of the light used is

The equivalent resistance between $A$ and $B$ will be :

A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by $T=2\pi \sqrt{\frac{l}{g^{\prime }}}$ , where g' is equal to

A coil of mean area $500{\text{cm}}^2$ and having $1000\text{turns}$, is held perpendicular to a uniform magnetic field of $0.4\times {10}^{-4}\text{T}$. The coil is turned through ${180}^{\circ }$ in $\frac{1}{10}\text{seconds}$. Calculate the average induced emf?

A platinum resistance thermometer reads $0^{\circ }$ when its resistance is 80 $\Omega$ and ${100}^{\circ }$ when its resistance is 90 $\Omega$. Find the temperature at the platinum scale at which the resistance is 86 $\Omega$

A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown. Initially the system is at rest when a particle of mass $m$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $v$, the speed with which the system moves just after collision is