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The time period of an artificial satellite in a circular orbit of radius R is 2 days and its orbital velocity is $v_0$. If time period of another satellite in a circular orbit is 16 days then

Find the minimum value of coefficient of friction between the $4\text{kg}$ block and the surface for the system to be at rest for the figure shown, (Block $A=4\text{kg}$ and block $B=3\text{kg}$)

Two particles A and B are moving with uniform velocity as shown in the figure given below at t =0.



Find out shortest distance between two particles.

The minimum energy required to launch a $m\text{kg}$ satellite from the earth’s surface in a circular orbit at an altitude $2R$, where $R$ is the radius of earth is

The light from a torch is normally incident on the surface at intensity of illumination $I_1$. If the surface is tilted to ${45}^{\circ }$ from initial position, then what will be intensity of illumination $I_2$ on the surface in terms of $I_1$ ?

The intensity of radiation emitted by the sun has its maximum value at a wavelength $510\text{nm}$ and that emitted by another star has the maximum value at $350\text{nm}$. If we treat them as black bodies, then the ratio of the surface temperature of the sun and the star is

A coil having an area $A_0$ is placed in a magnetic field. The field intensity changes from $B_0$ to $4B_0$ in time interval of ‘t’. The magnitude of emf induced in the coil will be _____.

A uniformly tapering vessel is filled with a liquid of density $900{\text{kg/m}}^3$. The force that acts on the base of the vessel due to the liquid (excluding atmospheric force) is : [Take $g=10{\text{m/s}}^2$]

A particle is suspended from a fixed point by a string of length $10\text{m}$. The particle is given a horizontal velocity at the lowest point. The string slacks after the particle have reached a height of $16\text{m}$ above the lowest point. What is the velocity of the particle just before the string slacks?

Three components of sinusoidal progressive waves travelling in the same direction along the same path having the same period, but with amplitudes $A,A/2$ and $A/3$. The phase of the vibration at any position $x$ on their path at time $t=0$ are $0,-\pi /2$ and $\pi$ respectively. Find the amplitude and phase of the resultant wave

A thin rod has a length of $5\text{m}$. What is the ratio of the $\text{MI}$ of the rod about an axis perpendicular and passing through it's centre, to $\text{MI}$ of the rod about an axis perpendicular and passing through one of the edges of the rod?

The brakes of a car moving at $20m/s$ along a horizontal road are suddenly applied and it comes to rest after travelling some distance. If the coefficient of friction between the tyres and the road is $0.90$, and it is assumed that all four tyres behave identically, find the shortest distance the car would travel before coming to a stop.

Different voltages are applied across a P-N junction and the currents are measured for each value. Which of the following graphs is obtained between voltage and current

Sodium and copper have work functions 2.3eV and 4.5eV respectively. Then the ratio of their threshold wavelengths is nearest to

Find the MOI of a uniform circular disc of mass $M=10\text{kg}$ and radius $R=10\text{m}$ about tangent perpendicular to its plane.

An infinite number of charges, each numerically equal to $q$ and of the same sign, are placed along the x-axis at $x=1\text{m},x=2\text{m},x=4\text{m},x=8\text{m}$ and so on. Then the electrical potential at $x=0$ due to this set of charges is ( Assume that $\frac{1}{4\pi {ϵ}_0}=k$)

A sphere of mass $m$ moving with a constant velocity $u$ hits another stationary sphere of some mass. If $e$ is the coefficient of restitution, then ratio of velocities of the two spheres $\frac{v_1}{v_2}$ after collision will be

The bob of a pendulum of mass ($m$) at rest is given a sharp hit to impart the horizontal velocity $\sqrt{6gl}$, where $l$ is the length of the pendulum.



Find the tension in the string at highest point?

Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 4.0 s. When one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves. Determine the speed of the wave.

A block $\left(B\right)$ is attached to two unstretched springs $S_1$ and $S_2$ with spring constant $2k$ and $4k$ respectively. The other ends are attached to two supports $m_1$ and $m_2$ not attached to the walls. The springs and supports have negligible mass and the surface is frictionless. The block $B$ is displaced towards wall $1$ by a small distance $x$ and released. The block returns and moves a maximum distance $y$ towards wall $2$. Displacement $x$ and $y$ is measured with respect to the equilibrium position of the block $B$. The ratio of $\frac{y}{x}$ is

Two uniform solid spheres held fixed of equal radii $R$, but mass $M$ and $4M$ have centre to centre separation $6R$. A projectile of mass $m$ is projected from the surface of the sphere of mass $M$ directly towards the centre of the second sphere. Obtain an expression for the minimum speed $v$ of the projectile so that it reaches the surface of the second sphere.

A steel wire of length $4.7\text{m}$ and cross-sectional area $3.0\times {10}^{-5}{\text{m}}^2$ stretches by the same amount as a copper wire of length $3.5\text{m}$ and cross-sectional area $4.0\times {10}^{-5}{\text{m}}^2$ under a given load. Find the ratio of the Young's modulus of steel to that of copper

Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8\text{m}$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of the second drop from the floor when the first drop strikes the floor.

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude $P_A$ inside the tube. If the atmospheric pressure is $P_0$ then the ratio of maximum and minimum pressure at the closed end of the tube will be

The spectrum of radiation $1.0\times {10}^{14}Hz$ is in the infrared region. The energy of one photon of this in joules will be

A particle of mass $m$ is moving with a constant velocity $v$ parallel to the $x-$ axis as shown in the figure. Its angular momentum (magnitude) about origin $\text{O}$ is

Which one of the following is not the unit of electric charge?

A ball is thrown from a point on a ground at some angle of projection. At the same time, a bird starts from a point directly above this point of projection at a height $h$, horizontally with speed ${}^{\prime }{u}^{\prime }$. Given that during its flight, the ball just touches the bird at only one point. Find the distance on the ground from the point of projection where the ball strikes.

Rain is falling vertically downwards with a velocity of $4km/h$. A man walks in the rain with a velocity of $3km/h$. The raindrops will fall on the man with a velocity of magnitude

The de-Broglie wavelength of a particle accelerated with a p.d of 150 V is ${10}^{-10}m$. If it is accelerated with a p.d of 600 V, its wavelength will be

In an isothermal reversible expansion if the volume of $96\text{g}$ of oxygen at ${27}^{\circ }\text{C}$ is increased from $70\text{L}$ of $140\text{L}$, then the work done by the gas will be

In the pulley system shown in the figure, the radii of the bigger and smaller pulleys are $2\text{m}$ and $1\text{m}$ respectively. Find the resultant torque at point $\text{O}$. (Take $g=10{\text{m/s}}^2)$

A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th sec to that covered in 5 sec is

In the figure shown, the charge on the capacitor is $q=\left(4t^2\right)\text{C}$ then $V_{ab}$ at $t=1\text{s}$ is

Two trains $A$ and $B$ simultaneously start moving along parallel tracks from a station along same direction. A starts with constant acceleration $2{\text{m/s}}^2$ from rest while $B$ with the same acceleration but with initial velocity of $40\text{m/s}$. Twenty seconds after the start, passenger of $A$ hears whistle of $B$. If frequency of whistle is $1194\text{Hz}$ and velocity of sound in air is $322\text{m/s}$, then the frequency observed by the passenger is

Match the block diagrams of block of mass m, with their corresponding free body diagram. (spring consent is kand x is change in spring length).

An up escalator is going at the rate of 10 step/min. How many steps per min should I move down on it as to look like that I am at rest to a person standing on ground.

You have prepared a nice sample of $N_{\circ }$ radioactive nuclei of decay constant $\lambda$, and want to show it off to your friends. When they arrive units of time later, you open the lid and find there are only _______ nuclei left intact.

One mole of an ideal gas undergoes a process in which $T=T_0+a{V}^3$, where $T_0$ and '$a$' are positive constants and $V$ is the volume. The volume for which the pressure of the gas will be minimum is

If a particle has velocity $v\left(t\right)=t^2-7t+12$, the average speed in $6\text{sec}$ is

The position of the centre of mass of a system consisting of two particles of masses $m_1$ and $m_2$, separated by distance $L$, from $m_2$ is

Which of the following is not an application of eddy currents?

A uniform square lamina of side 2a is hung up by one corner and oscillates in its own plane which is vertical. Find the length of the equivalent simple pendulum.

If a body is rotating about a given Axis and a Force is applied at any point on that body along any random direction, what can we say about the torque of this force about any point lying on its Axis of rotation?

A solid cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $K_2.$ The two ends of the combined system are maintained at two different temperatures. If there is no loss of heat across the cylindrical surface and the system is in steady state, the effective thermal conductivity of the system is:

An electron is accelerated through a potential difference of $10,000V$. Its de Broglie wavelength is (nearly) $\left(m_e=9\times {10}^{-31}kg\right)$