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A length L of wire carries a steady current I. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is

[NCERT 1980

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $\theta$, where $\theta$ is the angle by which it has rotated, is given as $k{\theta }^2$ (where $k$ is a constant). If its moment of inertia is $I$, then the angular acceleration of the disc is

The equation of a standing wave, produced on a string fixed at both ends, is $y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right]$

What could be the smallest length of the string?

A diminished virtual image can be formed only in

[MP PMT 2002]

de-Broglie wavelength of a body of mass 1 kg moving with velocity of 2000 m/s is

In an experiment, mass of an object is measured by applying a known force on it, and then measuring its acceleration. IF, in the experiment, the measured values of applied force and the measured acceleration are F = 10.0 $\pm$ 0.2N and a = 1.00 $\pm$ 0.01 m/s${}^2$, respectively, the mass of the object is

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to

Light of wavelength $4000\stackrel{\circ }{A}$ falls on a metal surface having work function of 2.0 eV. The stopping potential is

A wheel is rotating about a fixed axis through its center with 300 rpm. A constant torque starts acting on it opposes its motion. Before coming to rest it makes 25 complete rotations. If the moment of inertia of the wheel about the axis of rotation is $\frac{10}{\pi }Kg{m}^2$, the torque (in N-m) acting on it is

Two stereo speakers $S_1$ and $S_2$ are separated by a distance of $2.40\text{m}$. A person $\left(P\right)$ is at a distance of $3.20\text{m}$ directly in front of one of the speakers as shown in the figure. The frequency in the audible range$(20–20000\text{Hz})$ for which the listener can hear minimum sound intensity is (Take speed of sound in air as $320\text{m/s}$)

An electric heater is used in a room of total wall area $137{\text{m}}^2$ to maintain a temperature of ${20}^{\circ }\text{C}$ inside it when the outside temperature is $-{10}^{\circ }\text{C}.$ The walls have three layers of different materials. The innermost layer is of wood of thickness $2.5\text{cm}$, the middle layer is of cement of thickness $1.0\text{cm}$ and the outermost layer is of brick of thickness $2.5\text{cm}$. Find the power of the electic heater. Assume that there is no heat loss through the floor and ceiling. The thermal conductivities of wood, cement and brick are $0.125{\text{W/m}}^{\circ }\text{C}$, $1.5{\text{W/m}}^{\circ }\text{C}$ and $1.0{\text{W/m}}^{\circ }\text{C}$ respectively.

In an experiment for determination of refractive index of glass of a prism by i - $\delta$ plot, it was found that a ray incident at angle ${35}^{\circ }$, suffers a deviation of ${40}^{\circ }$ and that it emerges at angle ${79}^{\circ }$. In that case which of the following is closest to the maximum possible value of the refractive index?

Find the maximum value of $F$ such that both the blocks move together. Take $g=10{\text{m/s}}^2$.

A ‘U’ - tube containing a liquid is accelerated horizontally with a constant acceleration $a_0$. If the separation between the vertical limbs is l, the difference in the heights of the liquid in the two arms is

The amplitude of a wave represented by the displacement equation $y=\frac{1}{\sqrt{a}}\sin \omega t\pm \frac{1}{\sqrt{b}}\cos \omega t$ will be

The correct variation of pressure with depth $\left(x\right)$ is: [Assume the free surface to be the reference and conditions to be ideal]

A bomb at rest explodes into three equal fragments. Two fragments fly off at right angles with velocity $12\text{m/s}$ and $9\text{m/s}$. If the explosion process occurs in $0.1\text{s}$, find out the average force acting on the third particle, if total mass of the bomb is $12\text{kg}$.

Four holes of radius $R$ each are cut from a thin square plate of side $4R$ and mass $M$. The moment of inertia of the remaining portion about $z-$ axis (out of the plane) is

If a thermometer reads freezing point of water as ${20}^{\circ }$ and boiling point as ${150}^{\circ }$, how much does the thermometer read when the actual temperature is ${60}^{\circ }C$?

The equation of a wave travelling on a string is $y=4sin(4\pi t-\frac{\pi }{16}x)$ if x and y are in centimetres, then velocity of wave is

A bus is moving with a velocity of 5 m/s towards a huge wall. the driver sounds a horn of frequency 165 Hz. If the speed of sound in air is 355 m/s, the number of beats heard per second by a passenger on the bus will be approximately,

Consider the potentiometer circuit shown in the figure below. The potentiometer wire is 600 cm long. At what distance from point A should the jockey be placed to get zero deflection in the galvanometer?

If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are $a,b$ and $c$ respectively, then the corresponding ratio of increase in their lengths would be

A body of mass 'M' collides against a wall with a velocity v and retraces its path with the same speed. The change in momentum is (take initial direction of velocity as positive)

X-rays are incident normally on a crystal of lattice constant 0.6 nm. The first order reflection of diffraction from the crystal occurs at an angle of ${30}^{\circ }$. What is the wavelength of X-rays used?

The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which a car can be driven round a curve of radius 40 m without skidding is $(assumeg=10m{s}^{-2})$

Which of the following sets can't enter into the list of fundamental quantities in any system of units?

1)length,mass, velocity

2)length,time and velocity

3)mass ,time and velocity

4)length,time and mass

I think it is the second option because velocity is LT^-1 so there is no chance of putting velocity beside length and time.

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3. For this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

An object is in combined rotational and translational motion. Its K.E. is

If the critical angle for the medium of a prism is $C$ and the angle of prism is $A$, then there will be no emergent ray when

The P.E. of a particle executing SHM at a distance x from its equilibrium position is

For what minimum angular speed ${\omega }_{min}$ , will the mass m not slip on the wall?

A train starts from rest and moves with a constant acceleration of 2.0 $\frac{m}{s^2}$ fbr half a minute. The brakes are then applied and the train comes to rest in one minute. Find.

(a) the total distance moved. by the train,

(b) the maximum speed attained by the train and

(c) the position(s) of the train at half the maxim um speed

The light emitted in the transition n = 3 to n = 2 in hydrogen is called $H_a$ light. Find the maximum work function a metaln can have so that $H_a$light can emit photoelectrons from it.

Acceleration of the particle in a rectilinear motion is given as $a=3t^2+4t-3$ in $\left(m/s^2\right)$. The velocity of the particle as a function of time $t$ is
(Given, at $t=0,u=1m/s$)

The 200 m free style women's swimming gold medal at Seoul Olympics 1988 went to Heike Friedrich of East Germany when she set a new Olympic record of 1 minute and 57.56 seconds. Assume that she covered most of the distance with a uniform speed and had to exert 460 W to maintain her speed. Calculate the average force of resistance offered by the water during the swim.

An insulated solid sphere has a volume charge density ρ. ‘r’ is the distance of a point P from the Centre. Which graph represents the correct variation of electric field with respect to r?

What will happen to an electric dipole placed in a non uniform electric field

I know that the emision spectra for any substance always remains the same irrespective of the form it is present(solid,gas).Does it also applies for the absorption spectra

A rocket with an initial mass of $1000\text{kg}$ is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of $10\text{kg}$ per second. The burnt matter is ejected vertically downwards with a speed of $2000\text{m/s}$ relative to the rocket. If burning ceases after one minute, the maximum velocity of the rocket is

Figure shows a disc which is rolling without slipping. The magnitude and direction of frictional force acting on the disc is

Rank in order, from highest to lowest, the liquid heights $h_a,h_b,h_c\&h_d$ . The air flow is from left to right. The liquid columns are not drawn to scale but pipe diameter is drawn to scale.

A ball is dropped from a of height of 5m from ground. Find the velocity with which it hits the ground.