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A car goes around a flat curved road. Which of the following can provide for the centripetal force?

Calculate the ratio of the angular momentum of the earth about its axis due to its spinning motion to that about the sun due to its orbital motion. Radius of the earth = 6400 km and radius of the orbit of the earth about the sun = 1.5 $\times {10}^8$ km.

An elevator in which a man is standing is moving upwards with a speed of 10 m/s. If the man drops a coin from a height of 2.45 m from the floor of the elevator, it reaches the floor of the elevator after a time (g = 9.8 m/s2)

A particle is acted by a force F = kx, where k is a positive constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x

A particle is projected with a certain velocity at an angle $\alpha$ above the horizontal from the foot of an inclined plane of inclination ${30}^{\circ }$. If the particle strikes the plane normally. then $\alpha$ is equal to

The value of $n^{th}$ orbital radius is

By inserting a capillary tube upto a depth l in water, the water rises to a height h. If the lower end of the capillary is closed inside water and the capillary is taken out and closed end opened, to what height the water will remain in the tube(l>h)

Two small spheres each having the charge +Q are suspended by insulating threads of length L from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be

A small charged particle of mass m and charge q is suspended by an insulated thread in front of a very large conducting charged sheet of uniform charge density $\sigma$ . The angle made by the thread with the vertical in equilibrium is:

A point moves along an arc of a circle of radius R. Its velocity depends upon the distance covered `s' as $v=A\sqrt{s}$, where a is constant. The angle $\theta$ between the vector of total acceleration and tangential acceleration is:

A particle moves along $x-$axis in such a way that its $x-$ coordinate varies with time $t\left(\text{in s}\right)$ according to the equation: $x=(6-4t+6t^2)\text{m}$. The velocity of the particle will vary with time according to the graph

In a fission reaction ${}_{92}{U}^{236}\to X^{117}+Y^{117}+2_0{n}^1+\epsilon ,$ The binding energy per nucleon of X and Y is 8.5 MeV where as of ${}_{92}{U}^{236}$ is 7.6 MeV. The total energy liberated will be about

Two beads, each of mass ‘m’ slide from rest from the position shown along a smooth massless rod of length 2L. The rod is initially rotated with an angular velocity of $\sqrt{\frac{g}{L}}$ about the vertical axis. The speed of each bead at the time of leaving the rod is

Three plane mirrors are arranged mutually perpendicular to each other as shown in the figure. If a point object is placed symmetrically between the mirrors, then the number of distinct images formed will be

There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which has to be applied on the tank to keep it in equilibrium is

A street car moves rectilinearly from station A (here car stops) to the next station B (here also car stops ) with an acceleration varying according to the law $f=a-bx$, where $a$ and $b$ are positive constants and $x$ is the distance from station A. The distance between the two stations & the maximum velocity are respectively.

If $x$ grams of steam at ${100}^{\circ }C$ becomes water at ${100}^{\circ }C$ which converts y grams of ice at $0^{\circ }C$ into water at ${100}^{\circ }C$, then the ratio $\frac{x}{y}$ will be

A potentiometer wire of length $100cm$has a resistance of $10\Omega$. It is connected in series with an external resistance and a cell of emf $2V$ and negligible internal resistance. A source of emf $10mV$ is balanced against a length of $40cm$ of the potentiometer wire.Then the value of external resistance is

Find the change in internal energy of the system from state P to R, while moving from $P\to Q\to R$, if heat added to the system for the process $PQ$ and $QR$ is $300\text{J}$ each.

The variation of vapour pressure (b) as a function of temperature (a) is studied for $C_2{H}_{5}O{C}_2{H}_5,CC{l}_4,and{H}_{2}O$ at 760mm Hg and is shown in the figure below. The boiling temperature of $C_2{H}_{5}O{C}_2{H}_5,CC{l}_4,and{H}_{2}O$ are 308,350 and 373K respectively. Curves A,B, C respectively correspond to:

Let $E$, $G$ and $N$ represent the magnitudes of electromagnetic, gravitational and nuclear forces between two electrons at a given separation. Then

From the top of a tower of height (13/2)g , a body is projected having 6gms^-1 and 8gms^-1 as vertical and horizontal components of its initial velocity. Find the time of flight and the distance from the foot of the tower of the point at which it strikes the ground?

Which of the following facts suggests that light is a non-mechanical wave?

The curved part of the surface shown is semi-circular. All the surfaces are frictionless. Speed of the bigger block when the smaller block reaches the point $A$ of the surface is:

The displacement-time graph of a moving object is shown in Figure. Which of the following velocity-time graphs could represent the motion of the same body?

P-V diagram of an ideal gas is an shown in figure. Work done by the gas in the process ABCD is

One gram of ice ( 0° C ) is mixed with one gram of steam ( 100° C ). After thermal equilibrium, the temperature of the mixture is

Find the value of current in $10\omega$ resistance. (in Amperes)___

The kinetic energy of 5.6 litres of oxygen at STP in cals is

If E, G, J and m represent energy, universal gravitational constant, angular momentum and mass respectively, then dimensions of $\frac{E{J}^2}{m^5{G}^2}$ are those of:

Two electric bulbs rated $P_1$ watt – V volt and $P_2$ watt – V volt are connected in parallel and V volt are applied to it. The total power will be

A liquid of refractive index ${\mu }_0$. is filled between slits and screen. Initially the central maxima is at point O on screen, with no slabs in front of slits. Now two slabs of refractive index ${\mu }_1$ and ${\mu }_2$, with thickness $t_1$ and $t_2$ respectively are placed in front of slits as shown, So that the position of central maxima does not change.
Find the ratio of $\frac{t_1}{t_2},$ if ${\mu }_0=1.5,{\mu }_1=1.8$ and ${\mu }_2=2.1$___

A ball is dropped onto a fixed horizontal surface from height h₀. The coefficient of restitution is e. Find the total distance D travelled by the ball before it comes to rest on the surface.

A 10 kg body is acted upon by a conservative force $F=-2x-6x^{2}N$ and x in m. Take potential energy associated with the force to be zero at x = 0. If the object has a velocity of 4m/s in the negative x-direction when at x = 4m, what is its speed as it passes through the origin ( in m/s) ?

A force starts acting on a spring block system. At a stretch when $x=\frac{mg}{k}$

A cubical block is subjected to three forces $F_1=20\text{N}$ acting at an angle of ${45}^{\circ }$ with horizontal and lying in the diagonal plane of the cube, $F_2=30\text{N}$ along $y-$axis and $F_3=40\text{N}$ acting in the negative $x-$direction as shown. Find the magnitude of friction force acting on the body.

The equation for a wave travelling in $x$ direction on a string is given as
$y=10\sin (\pi t-0.5x)$, where $y$ and $x$ are in $\text{m}$ and time$\left(t\right)$ in $\text{sec}$. Find the acceleration of a particle at $x=\pi \text{m}$ at time $t=1\text{sec}$.

A charge particle of charge q, mass m is projected with a velocity $\overrightarrow{v}=v\hat{i}$ . The electric field $\overrightarrow{E}=E\hat{k}$ and magnetic field $\overrightarrow{B}=B\hat{j}$ is applied. The acceleration of the particle is

Using differentials, find the approximate value of the following up to 3 places of decimal.
$(32.15{)}^{\frac{1}{5}}$

A ball is thrown with a velocity of $40\text{m/s}$ at an angle of $60°$ with the horizontal from a point $A$ on the ground. A boy simultaneously starts from $A$ to move a constant velocity $v$ such that the ball is always overhead the boy. Then value of $v$ is

Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.

The Bat Life: What can be said with 100% confidence about the temperatures at point $P_{1}and{P}_2$?

A flywheel has an intial rotational kinetic energy equal to $10\text{J}$. A constant torque is applied on the flywheel and work done by the torque is $25\text{J}$. Find the final rotational kinetic energy of the flywheel.

When a bullet passed through a wooden plank it looses 1/20th of its velocity. The number of such bullets required to stop the bullet is?

The kinetic energy of a particle moving along a circle of radius $R$ depends on the distance covered $S$ as $K{S}^2$ where $K$ is a constant. Find the force acting on the particle as a function of $S$

Show that it is not possible for a photon to be completely absorbed by a free electron.