From a train moving with constant velocity `V`, a carriage on a road parallel to the track, at distance `d` from it is observed to move so as to appear always in line with a more distant fixed object whose distance from the track is `D`. What is velocity of the carriage

A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its angular momentum with respect to the origin.

A body of mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Calculate its angular momentum with respect to the origin?

A train blowing its whistle moves with a constant velocity v away from an observer on the ground. The ratio of the natural frequency of the whistle to that measured by the observer is found to be 1.2 . If the train is not rest and the observer moves away from it at the same velocity, this ratio would be given by

A train is moving at a constant speed V when its driverobserves another train in front of him on the same track and voing in the same direction with constant speed v . If the distance berween the trains is x . Trains is x then what should be the minimum retardation of the train so as to avoed collision?.

A positive charge +Q is fixed at a point A. Another positively charged particle of mass m and charge +q is projected from a point B with velocity u as shown in (Fig. 3.103). Point B is at a large distance from A and at distance d from the line A C. The initial velocity is parallel to the line A C. The point C is at a very large distance from A. Find the minimum distance (in meter) of +q from +Q during the motion. Take Q q = 4 pi epsilon_0 m u^2 d and d (sqrt(2) - 1) m . .

The locus of a point which moves difference of its distance from two fixed straight which are at right angles is equal to the distance from another fixed straight line is

The apparent wavelength of light from a star moving away from earth is observed to be 0.01% more than its real wavelength. The velocity of star is

A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant. Prove that its locus is an ellipse.

A stationary observer receiver a sound of frequency f_(0) = 2000 Hz .Sourece is moving with constant velocity on a road at some non-zero prependicular distance from observer . The apparent frequncy f varies with times as show in figure . Speed of sound = 300 m//s . Find the maximum apparent frequency.

A railway carriage of mass M_(c) filled with sand of mass M_(s) moves along the rails. The carriage is given an impulse and it starts with a velocity v_(0) . At the same time it is observed that the sand starts leaking through a hole at the bottom of the carriage at a constant mass rate lambda . Find the distance at which the carriage becomes empty and the velocity attained by the carriage at that time. (Neglect the friction along the rails).