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A transverse sinusoidal wave moves along a string in the positive $x-$direction at a speed of $10\text{cm/s}$. The wavelength of the wave is $0.5\text{m}$ and its amplitude is $10\text{cm}$. At a particular time $t$, the snapshot of the wave is shown in the figure. The velocity of a particle at $P$ when its displacement is $5\text{cm}$ along $y-$axis is

Consider regular polygons with number of sides $n=3,4,\mathrm{5.......}$ as shown in the figure. The center of mass of all the polygons is at height $h$ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is $\Delta$. Then $\Delta$ depends on $n$ and $h$ as

Find the angle of projection of a projectile motion having same values of horizontal component and vertical component of velocity of projection.

A child is sitting on a swing whose minimum and maximum heights from the ground are $0.75\text{m}$ and $2\text{m}$ respectively. Its maximum speed will be

A current carrying loop is placed in a uniform magnetic field, in four different orientations $I,II,III$ and $IV$. Arrange all of them in decreasing order of their potential energy.

Yellow
light emitted from a sodium lamp has a wavelength (λ)
of 580 nm. Calculate the frequency (ν)
and wave number ()
of the yellow light.

The pulleys and strings shown in the figure are smooth and of
negligible mass. For the system to remain in equilibrium, the angle

In Young's double slit experiment the phase difference between the waves reaching the central fringe and fourth dark fringe will be

A transverse wave is propagating along $+x$ direction. At $t=2s$, the particle at $x=4$ $m$ is at $y=2mm$. With the passage of time its $y$ coordinate increases and reaches to a maximum of $4mm$. The wave equation is (using $\omega$ and $k$ with their usual meanings)

In the arrangement shown $\theta$ is varied between $0$ to $\frac{\pi }{2}.$ ( If $f_c:$ contact force, $N$ : normal Reaction, $f$ : friction), then which of the following variations are correctly shown

1. 3

The densities of wood and benzene at $0^{\circ }C$ are 880 kg $m^3$ and 900 kg $m^{-3}$ respectively. The coefficients of volume expansion are $1.2\times {10}^{-3}{}^{\circ }{C}^{-1}$ for wood and $1.5\times {10}^{-3}{}^{\circ }C$ for benzene. At what temperature will a piece of wood just sink in benzene ?

A long solenoid of cross-sectional area $5{\text{cm}}^2$ is wound with $25$ turns per $\text{cm}$. It is placed co-axially inside a closely wrapped coil of $10$ turns with radius of $25\text{cm}$. The magnitude of emf induced in the coil, when the current through the solenoid is decreasing at a rate of $0.2\text{A/s}$ is -

A conducting wheel in which there are four rods of length $l=20\text{cm}$ as shown in the figure, is rotating with angular velocity $10\text{rad/s}$ in a uniform magnetic field of $2.5\text{T}$ perpendicular to the plane of wheel. The induced potential difference between its center and rim will be -

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the
same siren. The ratio of velocity of train B to that of train A is

A particle of mass $2\text{kg}$ is projected on horizontal ground with an initial velocity $u=20\text{m/s}$ making an angle ${60}^{\circ }$ with the vertical. Find out the angular momentum of the particle about the point of projection when it just strikes the ground. [in ${\text{kg m}}^2\text{/s}$]

The height and horizontal distance $x$ of a projectile are given by $y=(8t-5t^2)m$ and $x=6tm$ where $t$ is in seconds. Find the maximum height of a projectile.
(Take $g=10m/s^2$)

The radiation force experienced by a body exposed to radiation of intensity $I_0$, assuming the surface of the body to be perfectly absorbing is

A power transmission line feeds input power at $2300\text{V}$ to a step-down transformer with its primary windings having $4000$ turns. The output power is delivered at $230\text{V}$ by the transformer. If the current in the primary coil of the transformer is $5\text{A}$ and its efficiency is $90\%.$ The output current would be

Monochromatic light of frequency of $6\times {10}^{14}Hz$ is produced by a laser. Power emitted is $2\times {10}^{-3}W.$ Approximately how many photons per second are emitted by the source?

A horizontal force of $10N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is