An open carriage in a goods train is moving with a uniform velocity of 10 m/s. If the rain adds water with zero velocity at the rate of 5 kg/s, then the additional force required by the engine to maintain the same velocity of the train is

A motorcycle has to move with a constant speed on an overbridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point. a. what can its maximum velocity be for which the contact with the road is not broken at the highest point? b. If the motorcycle goes at speed 1/sqrt2 times the maximum found in part a. where will it lose the contact with the road? c. What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?

A motorcycle has to move with a consatnt speed on an overbridge which is in the form of as circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point. a. what can its maximum velocity be for which the contact with the road is not broken at the highest point? b. If the motorcycle goes at speed 1/sqrt2 times the maximum found in part a. where will it lose the contact with the road? c. What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?

A uniform disc of mass 1 kg and radius 20 cm is rolling purely on a flat horizontal surface. Its centre C is moving with acceleration a = 20 ms^(-2) and velocity v =4 m//s at a certain instant. At this instant. points A and B are located on the disc as shown in the diagram, with AC = BC = 10 cm . What is the acceleration magnitude of point A ?

A uniform disc of mass 1 kg and radius 20 cm is rolling purely on a flat horizontal surface. Its centre C is moving with acceleration a = 20 ms^(-2) and velocity v =4 m//s at a certain instant. At this instant. points A and B are located on the disc as shown in the diagram, with AC = BC = 10 cm . What is the acceleration magnitude of point B ?

A uniform disc of mass 1 kg and radius 20 cm is rolling purely on a flat horizontal surface. Its centre C is moving with acceleration a = 20 ms^(-2) and velocity v =4 m//s at a certain instant. At this instant. points A and B are located on the disc as shown in the diagram, with AC = BC = 10 cm . What is the kinetic energy of the disc?

The angular velocity of the engine (and hence of the wheel) on a scooter is proportional to the petrol input per second. The scooter is moving on a frictionless road with uniform velocity. If the petrol input is increased by 10% the linear velocity of the scooter is increased by

A cart loaded with sand moves along a horizontal floor due to a constant force F coinciding in direction with cart's velocity vector. In the process, the sand spills through a hole in the bottom with a constant rate mukg//s. Find the acceleration and velocity of the cart at the moment t , if at the initial moment t=0 the cart with loaded sand had mass m_(0) and its velocity was equal to zero. Friction is to be neglected.

A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration a along a straight horizontal track, the string supporting the bob makes an angle tan^1 (a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity, if the angle of incline is tan^-1(a/g) , the string again makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerated on a horizontal straight track or it is going on an incline? If yes, how? If no, suggest a method to do so.

In one-dimensional kinematics, a particle can move strictly along a straight line. The description of motion of the particle can be done in two ways: (i) mathematical equation and (ii) graphs. The choice of a particular method for solving a problem often depends upon the type and nature of problem, for example the graphical method provides more physical insight One dimensional motion is categorised into 1. motion with constant velocity 2. motion with constant acceleration, and 3. accelerated and de-accelerated motion If you represent inotion (1) by the graph on position time and velocity-time coordinates, the graphs may look like as given below. One very interesting case comes up, when a particle is thrown at a certain angle from the horizontal, the particle travels in the medium along a curved path, known as parabola. - The trajectory of the parabola written in the mathematical equation is given by y=xtantheta-(1)/(2)(gx^(2))/((v_0costheta))^(2) Ineglect resistance of medium and its motion where Vs and are the initial velocity of the projectile and the projection angle at the point of projection measured with the + x axis. There are some applications which we have seen in our life, like in many game shows, the theory of the projectile is always used An air gun is aimed at an elevated target, which is released in a free fall by some mechanism as the bullet leaves the nozzle. Irrespective of falling speed of object, the bullet will always hit the target. QOut of the two methods, graphical method and mathematical equation, which gives you the better precision