A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is : (use acceleration due to gravity g = 10 m/s2 and neglect air resistance)

The angle of projection of a particle is measured from the vertical axis as $\varphi$ and the maximum height reached by the particle is ${\mathrm{h}}_{\mathrm{m}}$. Here ${\mathrm{h}}_{\mathrm{m}}$ as function of $\varphi$ can be presented as

A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n{u}^2}{25g}$, where value of $n$ is: (Given, ' $g$ ' is the acceleration due to gravity.)

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between $t = 0$ to $t = 4s$?

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is ̱_______ km .

$$\text{Which of the following curves possibly represent one-dimensional motion of a particle? }$$ Choose the correct answer from the options given below :

The displacement x versus time graph is shown below. (A) The average velocity during 0 to 3 s is $10\mathrm{m}/\mathrm{s}$ (B) The average velocity during 3 to 5 s is $0\mathrm{m}/\mathrm{s}$ (C) The instantaneous velocity at $\mathrm{t}=2\mathrm{s}$ is $5\mathrm{m}/\mathrm{s}$ (D) The average velocity during 5 to 7 s and instantaneous velocity at $\mathrm{t}=6.5\mathrm{s}$ are equal (E) The average velocity from $t=0$ to $t=9\mathrm{s}$ is zero Choose the correct answer from the options given below :

A particle moves along the $x$-axis and has its displacement $x$ varying with time t according to the equation: $$x={\mathrm{c}}_0\left({\mathrm{t}}^2-2\right)+\mathrm{c}(\mathrm{t}-2{)}^2$$ where ${\mathrm{c}}_0$ and c are constants of appropriate dimensions. Then, which of the following statements is correct?

In an experiment with photoelectric effect, the stopping potential,

If $\lambda$ and $K$ are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be :

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3\times 10^{-11}\mathrm{m}$ while that for the electron in third excited state is $8.48\times 10^{-10}\mathrm{m}$. The ratio of the de Broglie wavelengths of electron in the ground state to that in the excited state is

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.Reason (R) : A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation.In the light of the above statements, choose the most appropriate answer from the options given below :

A light source of wavelength $\lambda$ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength $\frac{\lambda }{2}$, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )

Which of the following phenomena cannot be explained by wave theory of light?

A sub-atomic particle of mass $10^{-30}\mathrm{kg}$ is moving with a velocity $2.21\times 10^6\mathrm{m}/\mathrm{s}$. Under the matter wave consideration, the particle will behave closely like $\left(\mathrm{h}=6.63\times 10^{-34}\mathrm{J}.\mathrm{s}\right)$

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the em-wave? (Given $\mathrm{hc}=1242\mathrm{eVnm}$ where h is the Planck's constant and c is the speed of light in vaccum.)

An electron of mass ' m ' with an initial velocity $\overrightarrow{\mathrm{v}}={\mathrm{v}}_0\hat{i}\left({\mathrm{v}}_0>0\right)$ enters an electric field $\overrightarrow{\mathrm{E}}=-{\mathrm{E}}_{\mathrm{o}}\hat{\mathrm{k}}$. If the initial de Broglie wavelength is ${\lambda }_0$, the value after time t would be

In photoelectric effect, the stopping potential $\left({\mathrm{V}}_0\right)\mathrm{v}/\mathrm{s}$ frequency $(v)$ curve is plotted. ( h is the Planck's constant and ${\varphi }_0$ is work function of metal ) (A) ${\mathrm{V}}_0\mathrm{v}/\mathrm{s}v$ is linear. (B) The slope of ${\mathrm{V}}_0\mathrm{v}/\mathrm{s}v$ curve $=\frac{{\varphi }_0}{\mathrm{h}}$ (C) h constant is related to the slope of ${\mathrm{V}}_0\mathrm{v}/\mathrm{s}v$ line. (D) The value of electric charge of electron is not required to determine h using the ${\mathrm{V}}_0\mathrm{v}/\mathrm{s}v$ curve. (E) The work function can be estimated without knowing the value of $h$. Choose the correct answer from the options given below :

A proton of mass ' $m_P$ ' has same energy as that of a photon of wavelength ' $\lambda$ '. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.