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A string of length $l$ is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is $2\text{ mm}$. The amplitude of a particle at a distance $l/8$ from the fixed end is:
The angular width of the central maximum in the Fraunhofer diffraction for $\lambda = 6000 \text{ \AA}$ is $\theta_0$. When the same slit is illuminated by another monochromatic light, the angular width decreases by $30\%$. The wavelength of this light is:
The magnetic flux linked to a circular coil of radius R is given by: $\phi = 2t^3 + 4t^2 + 2t + 5$ Wb. What is the magnitude of the induced EMF in the coil at $t = 5$ s?
A source of sound S emitting waves of frequency $100 \text{ Hz}$ and an observer O are located at some distance from each other. The source is moving with a speed of $19.4 \text{ ms}^{-1}$ at an angle of $60^\circ$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330 \text{ ms}^{-1}$), is:
In the Young's double-slit experiment, the intensity of light at a point on the screen (where the path difference is $\lambda$) is $K$, where $\lambda$ is the wavelength of light used. The intensity at a point where the path difference is $\lambda/4$ will be
For a transparent medium, relative permeability and permittivity, $\mu_r$ and $\varepsilon_r$ are 1.0 and 1.44 respectively. The velocity of light in this medium would be:
An unpolarised light beam strikes a glass surface at Brewster's angle. Then:
Twenty seven drops of same size are charged at $200 \text{ V}$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop.
The equation of state of some gases can be expressed as (P + a/V²)(V − b) = RT. Here P is the pressure, V is the volume, T is the absolute temperature and a, b, R are constants. The dimensions of ‘a’ are:
A linearly polarized monochromatic light of intensity 10 lumen is incident on a polarizer. The angle between the direction of polarization of the light and that of the polarizer such that the intensity of output light is 2.5 lumen is:
A student measured the diameter of a small steel ball using a screw gauge of least count $0.001\text{ cm}$. The main scale reading is $5\text{ mm}$ and zero of circular scale division coincides with $25$ divisions above the reference level. If the screw gauge has a zero error of $-0.004\text{ cm}$, the correct diameter of the ball is:
A wave in a string has an amplitude of $2 \text{ cm}$. The wave travels in the positive direction of the x-axis with a speed of $128 \text{ m/s}$ and it is noted that $5$ complete waves fit in the $4 \text{ m}$ length of the string. The equation describing the wave is:
A beam of light of $600\text{ nm}$ from a distant source falls on a single slit $1\text{ mm}$ wide and the resulting diffraction pattern is observed on a screen $2\text{ m}$ away. The distance between first dark fringes on either side of the central bright fringe is
The decreasing order of the wavelength of infrared, microwave, ultraviolet and gamma rays is:
The electric and the magnetic field, associated with an electromagnetic wave, propagating along the $+z$-axis, can be represented by:
In Young's double-slit experiment, a student observes 8 fringes in a certain segment of the screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen is:
Unit of energy in SI system is
Light with an energy flux of $25 \times 10^4 \text{ W m}^{-2}$ falls on a perfectly reflecting surface at normal incidence. If the surface area is $15 \text{ cm}^2$, the average force exerted on the surface is:
The length of the string of a musical instrument is $90\text{ cm}$ and has a fundamental frequency of $120\text{ Hz}$. Where should it be pressed to produce a fundamental frequency of $180\text{ Hz}$?
If an unpolarised light is incident on a plane surface of refractive index √3 at Brewster's angle, then the angle of refraction is: