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In which case, the nature of the image will be virtual, erect and enlarged ?

Why are the components of a single vector considered perpendicular to each other ?

Is 6 kg object is suspended by a vertical string from the ceiling of an elevator which is accelerating upwad 2.18 metre per second square, what is the tension in the string?

[MP PMT 1994, 95; DCE 1999, 2001; AIIMS 2001]

If a particle moving in a straight line which has slope $4$ and passes through $(4,-3)$, then, the equation of the motion is

With a concave mirror, an object is placed at a distance $x_1$ from the principal focus, on the principal axis. The image is formed at a distance $x_2$ from the principal focus. The focal length of the mirror is

A parallel plate capacitor of capacitance $90pF$ is connected to a battery of emf $20V$. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be

Average life of a radioactive sample is 4 ms. Initially the total number of nuclei is $N_{\left(0\right)}$ A charged capacitor of capacity $20\mu F$ is connected across a resistor R. The value of R such that ratio of number of nuclei remaining to charge on capacitor remains constant with respect to time is

A particle has a rectilinear motion and the figure gives its displacements as a function of time.

Which of the following statements are true with respect to the motion?

Two stones are thrown up simultaneously from the edge of a cliff with initial speeds v and 2v. The relative position of the second stone with respect to first varies with time till both the stones strike the ground as:

The amplitude of the function 3sin x

A rectangular blade of negligible weight floats on a water surface of surface tension $\frac{1}{7}\times {10}^{-1}N/m$. If the minimum force to lift up blade from water surface is $2\times {10}^{–2}N$, then find the internal perimeter of blade. [Take a = 10 cm]

A tube open at only one end is cut into two tubes of non equal lengths. The piece open at both ends has a fundamental frequency of 450 Hz and other has a fundamental frequency of 675 Hz. If the 1st overtone frequency of the original tube is 101.25 n Hz, then the value of n is: ___

The ratio of intensities between two coherent sound sources is 4 : 1. The difference of loudness in decibel (dB) between maximum and minimum intensities, when they interfere in space is

A boy of mass 40 kg is climbing a vertical pole at a constant speed. If the coefficient of friction between his palms and the pole is 0.8 and $g=10m{s}^{-2}$, the horizontal force that he is applying on the pole is

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A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $\omega$ is an example of a non-inertial frame of reference. The relationship between the force ${\overrightarrow{F}}_{\text{rot}}$ experience by a particle of mass $m$ moving on the rotating disc and the force ${\overrightarrow{F}}_{\text{in}}$ experienced by the particle in an inertial frame of reference is

${\overrightarrow{F}}_{\text{rot}}={\overrightarrow{F}}_{\text{in}}+2m({\overrightarrow{v}}_{\text{rot}}\times \overrightarrow{\omega })+m(\overrightarrow{\omega }\times \overrightarrow{r})\times \overrightarrow{\omega },$



where ${\overrightarrow{v}}_{\text{rot}}$ is the velocity of the particle in the rotating frame of reference and $\overrightarrow{r}$ is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter of a disc of radius $R$ rotating counterclockwise with a constant angular speed $\omega$ about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the $x-$axis along the slot, the $y-$ axis perpendicular to the slot and the $z-$ axis along the rotation axis $\overrightarrow{\omega =\omega \overrightarrow{k}}$. A small block of mass $m$ is gently placed in the slot at $\overrightarrow{r}=\left(R/2\right)\overrightarrow{i}$ at $t=0$ and is constrained to move only along the slot.





The distance $r$ of the block at time $t$ is

The length of the second pendulum on the surface of earth is 1 m. The length of seconds pendulum on the surface of moon, where g is 1/6th value of g on the surface of earth, is

If the bond dissociation energies of $XY,X_2$ and $Y_2$ (all diatomic molecules) are in the ratio of 1 : 1 : 0.5 and ${\Delta }_{f}H$ for the formation of $XY$ is $-200\text{kJ/mol}$, the bond dissociation energy of $X_2$ will be:

Four particles of masses m, m, 2m and 2m are placed at the four corners of a square of side a as shown in the figure. The (x, y) coordinates of the centre of mass are

Find the maximum and minimum value of $y=1+2sinx$ respectively.

Starting from rest, a body slides down a ${45}^{\circ }$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of kinetic friction between the body and the inclined plane is

A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

A car is moving with a speed of $60\text{m/s}$ on a curved road banked at an angle of ${45}^{\circ }$. If the coefficient of static friction between the wheels of the vehicle and the road is $0.4$, what should be the minimum radius of turn for the car so that it does not skid? Take $g=10{\text{m/s}}^2$.

Potentiometer wire is $100\text{cm}$ long and a constant potential difference is maintaned across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at $50\text{cm}$ and $10\text{cm}$ from the positive end of the wire in the two cases. The ratio of emf's is:

A simple harmonic wave is represented by the relation
$y(x,t)=A\sin 2x(vt-\frac{x}{\lambda })$
If the maximum particle velocity is three times the wave velocity, the wavelength $\lambda$ of the wave is

Explain briefly any three measures to overcome the communication barriers.

An L-shpaed lamina is shown in the figure given below:


Both rectangular sheets are made of the same material of negligible thickness. Find the $y$ coordinate of $\text{COM}$ of the system.

A conducting circular loop having a radius of 5.0 cm, is placed perpendicular to a magnetic field of 0.50 T. It is removed from the field in 0.50 s. Find the average emf produced in the loop during this time.

Two sources of sound, $S_1$, and $S_2$, emitting waves equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to $S_1,S_2$ and at a distance of 20.0 cm from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through Which the detector should be shifted to detect a minimum of sound.

In the decay ${}^{64}Cu{\to }^{64}Ni+e^{+}+v$, the maximum kinetic energy carried by the positron is found to be 0.650 MeV. (a) What is the energy of the neutrino which was emitted together with a positron of kinetic energy 0.150 MeV? (b) What is the momentum of this neutrino in kg m $s^{-1}$ ? Use the formula applicable to a photon.

The plastics if are hard, become soft and readily workable by addition of certain compounds called

A single battery fo emf E and internal resistance r is equivalent to a parallel combination of two batteries of emfs $E_1=2V$ and $E_2=1.5V$ and internal resistances $r_1=1\Omega$ and $r_2=2\Omega$ respectively, with polarities as shown in the figure.

(IIT-JEE 1997)

Fig. Shows the vertical section of a frictionless surface. A block of mass 2 kg is released from rest from position A; its KE as it reaches position C is $(g=10m{s}^{-2})$

The graph below shows power $\left(P\right)$ delivered by the engine of a car as a function of time.


Find out the final velocity of car, if initial velocity of the car is $10\text{m/s}$ and mass is $200\text{kg}$.

Infinite number of masses, each $2kg$, are placed along the $X-$ axis at $x=\pm 1m,\pm 2m,\pm 4m,\pm 8m,\pm 16m...$
The magnitude of the resultant gravitational potential in terms of gravitational constant $G$ at the origin $(x=0)$ is

If a current of 3 amperes flowing in the primary coil is reduced to zero in 0.001second, then the induced e.m.f in the secondary coil is 15000 volts. The mutual inductance between the two coils is

If an electron and a photon propagate in the form of waves having the same wavelength, it implies that they have the same

The figure shows four wire loops, with edge lengths of either $Lor2L$. All four loops will move through a region of uniform magnetic field $\overrightarrow{B}$ (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the e.m.f.$\left(e\right)$ induced as they enter the field.