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A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R$. The angle of projection, $\theta$, is then given by :
A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of
In a Young's double slit experiment, a student observes $8$ fringes in a certain segment of screen when a monochromatic light of $600\text{ nm}$ wavelength is used. If the wavelength of light is changed to $400\text{ nm}$, then the number of fringes he would observe in the same region of the screen is
A cup of coffee cools from $90^{\circ}C$ to $80^{\circ}C$ in $t$ minutes, when the room temperature is $20^{\circ}C$. The time taken by a similar cup of coffee to cool from $80^{\circ}C$ to $60^{\circ}C$ at a room temperature same at $20^{\circ}C$ is
In the product $\vec{F} = q(\vec{v} \times \vec{B}) = q\vec{v} \times (B\hat{i} + B\hat{j} + B_0\hat{k})$. For $q = 1$ and $\vec{v} = 2\hat{i} + 4\hat{j} + 6\hat{k}$ and $\vec{F} = 4\hat{i} - 20\hat{j} + 12\hat{k}$. What will be the complete expression for $\vec{B}$?
An electromagnetic wave of wavelength '$\lambda$' is incident on a photosensitive surface of negligible work function. If 'm' mass is of photoelectron emitted from the surface has de-Broglie wavelength $\lambda_d$, then
Two transparent media A and B are separated by a plane boundary. The speed of light in those media are $1.5 \times 10^8$ m/s and $2.0 \times 10^8$ m/s, respectively. The critical angle for a ray of light for these two media is
From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is
An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is
The displacement-time graphs of two moving particles make angles of $30^\circ$ and $45^\circ$ with the x-axis as shown in the figure. The ratio of their respective velocity is
Equation of displacement for any particle is $s = 3t^3 + 7t^2 + 14t + 8$ m. Its acceleration at time $t = 1$ sec is:
A body of mass $m$ is kept on a rough horizontal surface (coefficient of friction = $\mu$). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\vec{F}$, where:
If a square loop ABCD carrying a current i is placed near and coplanar with a long straight conductor XY carrying a current I, what will be the net force on the loop?
In which of the following processes, heat is neither absorbed nor released by a system?
The unit of e.m.f. is:
A big circular coil with $1000$ turns and an average radius of $10 \text{ m}$ is rotating about its horizontal diameter at a rate of $2 \text{ rad s}^{-1}$. The vertical component of the Earth's magnetic field at that location is $2 \times 10^{-5} \text{ T}$, and the electrical resistance of the coil is $12.56 \Omega$. The maximum induced current in the coil will be:
A square loop with a side length of $1 \text{ m}$ and resistance of $1 \Omega$ is placed in a uniform magnetic field of $0.5 \text{ T}$. The plane of the loop is perpendicular to the direction of the magnetic field. The magnetic flux through the loop is:
Dimensions of charge are:
A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4 \text{ m s}^{-1}$. The ball strikes the water surface after $4 \text{ s}$. The height of bridge above water surface is (Take $g = 10 \text{ m s}^{-2}$)
A full wave rectifier circuit consists of two p-n junction diodes, a centre-tapped transformer, capacitor and a load resistance. Which of these components remove the ac ripple from the rectified output?