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An automobile of mass m accelerates, starting from rest, while the engine supplies constant power P, its position varies with respect to time as?

A ring of uniform charge with radius 0.5 m having a 0.02 m gap, carries a charge +1C. The electric field at the centre is:

A charged particle enters a uniform magnetic field with velocity vector making an angle of ${30}^{\circ }$ with the magnetic field. The particle describes a helical trajectory of pitch x. The radius of the helix is

Two blocks of masses $m$ and $2m$ are kept on a smooth horizontal surface. They are connected by an ideal spring of force constant $k$. Initially the spring is unstretched. A constant force is applied to the heavier block in the direction shown in figure. Suppose at time $t$ displacement of smaller block is $x$, then displacement of the heavier block at this moment would be:

A wire has a resistance of $3\Omega$ at ${40}^{\circ }$C and resistance of $5\Omega$ at ${100}^{\circ }$C. The temperature coefficient of resistance of the wire is

An inductance of $\frac{200}{\pi }$mH,a capacitance of $\frac{{10}^{-3}}{\pi }$F and a resistance of 10$\Omega$ are connected in series with a.c. source 200V,50Hz.The phase angle of the circuit for current and voltage source is:

A uniform disc of mass 500 kg and radius 2 m is rotating at the rate of 600 r.p.m. What is the torque required to rotate the disc in the opposite direction with the same angular speed in a time of 100 second ?

The figure shows a circular loop made of a wire of radius R. The resistivity of the material varies as a function of $\theta$ such that $\rho ={\rho }_{0}si{n}^2\theta .$ The positions of the jockey such that the magnetic field at the center (o) due to the current in the loop is zero, will be

Two cells of emfs $E_1\text{and}{E}_2$ and internal resistances $r_1\text{and}{r}_2$ when connected in series and across an external resistance R give a current of 2A. When the polarity of one of the cells is reversed, the current through R is 1A. The ratio $E_1/E_2$ =

If a fish moving in upward direction in water with $9\text{m/s}$ is observing a bird which is diving in air $12\text{m/s}$ then calculate speed of bird as seen by fish - $({\mu }_{\text{water}}=\frac{4}{3})$
(correct answer + 1, wrong answer - 0.25)

Consider the mass distribution of 3 kg at $(0,0)$, 4 kg at $(0,4)$ & 5 kg at $(3,0)$. Where should a fourth mass of 8 kg be placed, so that centre of mass of complete arrangement will be at $(0,0)$?

A spherical shell of radius 10 cm is carrying a charge q. if the electric potential at distances 5 cm, 10 cm and 15 cm from the centre of the spherical shell is $V_1,V_{2}and{V}_3$ respectively, then

Okay I will give you another easy one. Just one last.
Find the angular momentum of the electron in $2^{nd}$ orbit of $H{e}^{+}$ ion.

A narrow beam of light of diameter D falls on a hemispherical glass sphere of radius R (R >>> D) and refractive index $\frac{3}{2}$. Diameter of beam on the base of hemisphere is.

Air streams horizontally past an air plane. The speed over the top surface is $60\text{m/s}$ and that under the bottom surface is $45\text{m/s}$. The density of air being $1.293{\text{kg/m}}^3$, calculate the difference in pressure across the wing.

A block of mass $0.18kg$ is attached to a spring of force-constant $2N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially the block is at rest and the spring is unstretched. The block slides to a distance of $0.06m$ and stops for the first time when an impulse is given to the block as shown in the figure. Then the initial velocity of the block (in $m/s$) is

A brass cube of side $a$ and density $\sigma$ is floating in mercury of density $\rho$. If the cube is slightly displaced vertically, it executes $SHM$. Its time period will be

The length of a sonometer wire is $0.75\text{m}$ and density is $9\times {10}^3{\text{kg/m}}^3$. It can bear a stress of $8.1\times {10}^8{\text{N/m}}^2$ without exceeding elastic limit. The fundamental frequency that can be produced in the wire is

In the circuit shown if switch S is closed at $t=0$, then $i_1$ and $i_2$ be the current at any finite time $t$. The ratio $\frac{\left(i_1\right)}{\left(i_2\right)}$ is

A particle moves on a straight line and its a - t graph is shown.
List - I gives some quantites and List - II gives some possible magnitudes of quantites then correct match is

$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{I) Average velocity of 4 sec}& \text{P) 0}\\ \text{II) Average acceleration of 4 sec}& \text{Q) 5}\\ \text{III) Displacement in 4 sec}& \text{R) 10}\\ \text{IV) Velocity at t = 4 sec}& \text{S) 20}\\ & \text{T) 40}\\ & \text{U) 50}\end{array}$

A satellite moves in elliptical orbit about a planet. Its maximum and minimum velocities are $3\times {10}^{4}m/s$ and $1\times {10}^{3}m/s$ respectively. What is the minimum distance of satellite from planet if maximum distance is $4\times {10}^4\text{km}$?

The particles each of mass $M$, are located at the vertices of an equilateral triangle of side $a$. At what speed must they move, if they revolve under the influence of their gravitational force of attraction in a circular orbit, circumscribing the triangle while still preserving the equilateral triangle?

The approximate depth of an ocean is $3500\text{m}$. The compressibility of water is $50\times {10}^{-11}{\text{Pa}}^{-1}$ and density of water is ${10}^3{\text{kg/m}}^3$. Find the fractional compression of water that will be obtained at the bottom of the ocean. (Take $g=10{\text{m/s}}^2$)

A carbon resistor is as shown below.
The resistance of it is

A mono atomic gas at a pressure p, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is $(\gamma =\frac{5}{3})$ :

What are the dimensions of $a$ and $b$ in the relation $F=a\sqrt{x}+b{t}^2$ where $F$ is force, $x$ is distance and $t$ is time?

A particle executes SHM with amplitude 0.2m and time period 24 sec. The time required by it to move from mean position to a point 0.1 m from the mean position is:

Two masses $M_1$ & $M_2$ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently due to gravitational attraction between them, their relative velocity of approach at a separation $d$ is

A projectile is thrown at $40\sqrt{2}\text{m/s}$ with an angle ${45}^{\circ }$ with horizontal. What will be the magnitude of velocity of the projectile after $1\text{sec}$ of its journey.

A body covers the first $\frac{1}{3}$ part of its journey with the speed of $2m/s$, next $\frac{1}{3}$ part with the speed of 3 m/s and the rest of the journey with a speed $6m/s$. The average speed of the body will be

A man is sitting on the shore of a river. He is in the line of a 1.0 m long boat and is 5.5 m away from the center of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of Projection and the edge of the boat are in the same horizontal level.

A wheel has initial angular speed of $\pi \text{rad/s}$. A constant force is acting on wheel to stop it. If wheel covers $\theta =\frac{\pi }{2}\text{rad}$ before coming to rest, find the magnitude of angular acceleration of the wheel.

A body of mass 10 $kg$ is slipping on a rough horizontal plane and moves with a deceleration of 4.0 $m/s^2$ What is the magnitude of frictional force?

If the force on a rocket, moving with a velocity $500\text{m/s}$ is $400\text{N}$, the rate of combustion of the fuel will be:

If the frequency of light in a photoelectric experiment is doubled, the stopping potential will

A car travel first $\frac{1}{3}rd$ of the total distance at $30\text{km/hr}$, next $\frac{1}{3}rd$ of the total distance at $40\text{km/hr}$ and last $\frac{1}{3}rd$ of the total distance at $24\text{km/hr}$. It's average speed in $\text{km/hr}$ for the whole Journey is

A horizontal uniform rod of mass ${}^{\prime }{m}^{\prime }$ has its left end hinged to the fixed incline plane, while its right end rests on the top of a uniform cylinder of mass ${}^{\prime }{m}^{\prime }$ which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest.


The ratio of magnitude of frictional force on the cylinder due to the rod and the magnitude of frictional force on the cylinder due to the inclined plane is:

Assuming that the atmosphere has the same density anywhere as at sea level $(\rho =1.3{\text{kg/m}}^3)$ and $g$ to be constant $(g=10{\text{m/s}}^2)$, what should be the approximate height of the atmosphere so that the atmospheric pressure at sea level is $p_0=1.01\times {10}^5{\text{N/m}}^2$ ?

A body starts from rest and moves along a straight line path with uniform acceleration . What is the ratio of velocities at t =1s and t=2s ?

There is some change in length when a $33000\text{N}$ tensile force is applied on a steel rod of area of cross section ${10}^{-3}{\text{m}}^2$. The change of temperature required to produce the same elongation, if steel rod is heated, is: (The modulus of elasticity is $3\times {10}^{11}{\text{N/m}}^2$ and the coefficient of linear expansion of steel is $1.1\times {{10}^{-5}}^{\circ }{C}^{-1}$)

An airplane flying horizontally at a constant speed of 350 km/h over level ground releases a bundle of food supplies. Ignore the effect of the air on the bundle.What are the bundle’s initial (a) vertical and (b) horizontal components of velocity? (c) What is its horizontal component of velocity just before hitting the ground? (d) If the airplane’s speed were, instead, 450 km/h, would the time of fall be longer,shorter,or the same?

The height of water level in a tank is $H=100\text{cm}$. The water stream is coming out of a hole at the depth of $20\text{cm}$ from top surface of water. Find out the time taken by the water coming out of the hole to reach the ground and the horizontal range of water. (Take $g=1000{\text{cm/s}}^2$)

An oil drop falls through air with a terminal velocity of $5\times {10}^{-4}\text{m/s}$. The radius of the drop will be:

Neglect density of air compared to that of oil. (Viscosity of air $=\frac{18\times {10}^{-5}}{5}{\text{N.s/m}}^2,g=10{\text{m/s}}^2$, density of oil $=900{\text{kg/m}}^3$

A thin uniform rod of mass $10\text{kg}$ is rotating about an axis passing through the end point of the rod of length $6\text{m}$ as shown in figure. Find the moment of inertia of the rod about this axis.

If a circuit is in a steady state, do all capacitors in that circuit carry equal amount of charge? If so, why?