A uniformly charged disc of radius R having surface charge density $$\sigma$$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-

Figure shows a rod AB, which is bent in a 120$${}^{\circ }$$ circular arc of radius R. A charge ($$-$$Q) is uniformly distributed over rod AB. What is the electric field $$\overrightarrow{E}$$ at the centre of curvature O ?

Two particles A and B having charges 20$$\mu$$C and $$-$$5$$\mu$$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

Choose the incorrect statement : (1) The electric lines of force entering into a Gaussian surface provide negative flux. (2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same. (3) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. (4) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given below

A cube is placed inside an electric field, $$\overrightarrow{E}=150y^2\hat{j}$$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :

The trajectory of a projectile in a vertical plane is y = $$\alpha$$x $$-$$ $$\beta$$x2, where $$\alpha$$ and $$\beta$$ are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $$\theta$$ and the maximum height attained H are respectively given by :

A mosquito is moving with a velocity $$\overrightarrow{v}=0.5t^2\hat{i}+3t\hat{j}+9\hat{k}$$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?

A butterfly is flying with a velocity $$4\sqrt{2}$$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

A player kicks a football with an initial speed of 25 ms$$-$$1 at an angle of 45$${}^{\circ }$$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms$$-$$2)

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

The ranges and heights for two projectiles projected with the same initial velocity at angles 42$${}^{\circ }$$ and 48$${}^{\circ }$$ with the horizontal are R1, R2 and H1, H2 respectively. Choose the correct option :

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is :

A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is :

A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of {{{t_1}} \over {{t_2}}} wil be :

The velocity-displacement graph describing the motion of bicycle is shown in the figure. The acceleration-displacement graph of the bicycle's motion is best described by :

A car accelerates from rest at a constant rate $$\alpha$$ for some time after which it decelerates at a constant rate $$\beta$$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

The velocity of a particle is v = v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1) is :

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to {{81} \over {100}} of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms$$-$$2)