Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30o. The electric field in the region shown between them is given by :

In finding the electric field using Gauss Law the formula \left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}} is applicable. In the formula $${\epsilon }_0$$ is permittivity of free space, A is the area of Gaussian surface and qenc is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?

Three charged particle A, B and C with charges –4q, 2q and –2q are present on the circumference of a circle of radius d. the charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is :

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

An electric dipole of moment $$\overrightarrow{p}=\left(-\hat{i}-3\hat{j}+2\hat{k}\right)\times 10^{-29}$$ C.m is at the origin (0, 0, 0). The electric field due to this dipole at $$\overrightarrow{r}=+\hat{i}+3\hat{j}+5\hat{k}$$ (note that $$\overrightarrow{r}.\overrightarrow{p}=0$$ ) is parallel to :

Two charged thin infinite plane sheets of uniform surface charge density $${\sigma }_{+}$$ and $${\sigma }_{-}$$, where |$${\sigma }_{+}$$| > |$${\sigma }_{-}$$|, intersect at right angle. Which of the following best represents the electric field lines for this system :

Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1) and E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1 (on S1) / V2 (on S2) of the electrostatic potentials on each sphere is :

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + $$\beta$$)v, this angle changes to 45o. The value of $$\beta$$ is close to :

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distanced (point B) from A (see figure) sees it at an angle 45o with respect to the vertical. When the balloon climbs up a further height h2, it is seen at an angle 60o with respect to the vertical if the girl moves further by a distance 2.464 d(point C). Then the height h2 is (given tan 30o = 0.5774)

Starting from the origin at time t = 0, with initial velocity 5$$\hat{j}$$ ms-1 , a particle moves in the x-y plane with a constant acceleration of $$\left(10\hat{i}+4\hat{j}\right)$$ ms-2. At time t, its coordinates are (20 m, y0 m). The values of t and y0 are, respectively:

A particle moves such that its position vector $$\overrightarrow{r}\left(t\right)=\cos \omega t\hat{i}+\sin \omega t\hat{j}$$ where $$\omega$$ is a constant and t is time. Then which of the following statements is true for the velocity $$\overrightarrow{v}\left(t\right)$$ and acceleration $$\overrightarrow{a}\left(t\right)$$ of the particle :

A particle starts from the origin at t = 0 with an initial velocity of 3.0 $$\hat{i}$$ m/s and moves in the x-y plane with a constant acceleration $$\left(6\hat{i}+4\hat{j}\right)$$ m/s2 . The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D meters. The value of D is :-

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is :

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to : [g is the acceleration due to gravity]

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/ hour. Speed (in ms–1) of this person as observed from train B will be close to : (take the distance between the tracks as negligible)

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height {h \over 2}. The velocity versus height of the ball during its motion may be represented graphically by : (graph are drawn schematically and on not to scale)

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is :

Given figure shows few data points in a phot electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surface is: (Plancks constant h = 6.62 × 10–34 J.s)

In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased :