Fill in the blanks using one of the words : at rest, in motion.
A person sitting in a compartment of a moving train is ............. relative to the other person sitting by his side and is............. relative to the platform.

Fill in the blanks using one of the words : at rest, in motion. A person walking in a compartment of a stationary train is ......... relative to the compartment and is ....... relative to the platform

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.

Figure shows the system is at rest initially with x = 0 , A man and a woman both are initially at the extreme carrier of the platform. The man and the woman start to move towards each other. Obtain an expression for the displacement s of the platform when the two meet in terms of the displacement x_1 of the man relative to the platform.

A uniform bar of length 12L and mass 48m is supported horizontally on two fixed smooth tables as shown in figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16m is sitting on the other end B. Both the insects moving towards each other along the rod with moth moving at speed 2v and the spider at half this speed (absolute). They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity v/2 relative to the rod towards the end A. The spider takes negligible time in eating on the other insect. Also, let v=L/T where T is a constant having value 4s . After starting from end B of the rod the spider reaches the end A at a time

A uniform bar of length 12L and mass 48m is supported horizontally on two fixed smooth tables as shown in figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16m is sitting on the other end B. Both the insects moving towards each other along the rod with moth moving at speed 2v and the spider at half this speed (absolute). They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity v/2 relative to the rod towards the end A. The spider takes negligible time in eating on the other insect. Also, let v=L/T where T is a constant having value 4s . By what distance the centre of mass of the rod shifts during this time?

A uniform bar of length 12 L and mass 48 m is supported horizontally on two smooth tables as shown in the figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16 m is sitting on the other end B . Both the insects start moving towards each other along the rod with moth moving at speed 2v and the spider at half of this speed. They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity v//2 relative to the rod towards the end A . The spider takes negligible time in eating the insect. Also, let v = L//T , where T is a constant having value 4 sec .The speed of the bar after the spider eats up the moth and moves towards A is

A person standing on a platform finds that a train moving with velocity, 0.6c takes one second to pass by him. Find (a) the length of the train as seen by the person and (b) the rest length of the train .

Two persons, A of mass 60 kg and B of mass 40 kg , are standing on a horizontal platform of mass 50 kg . The platform is supported on wheels on a horizontal frictionless surface and is initially at rest. Consider the following situations. (i) Both A and B jump from the platform simultaneously and in the same horizontal direction. (ii) A jumps first in a horizontal direction and after a few seconds B also jumps in the same direction. In both the situations above, just after the jump, the person ( A or B ) moves away from the platform with a speed of 3 m//s relative to the platform and along the horizontal. In situation (i), just after both A and B jump from the platform, velocity of centre of mass of the system ( A, B and the platform) is

A tank, with a square base of area 1 .0 m^(2) is divided by a vertical partition has a small hinged door of aren 20 cm^(2) . The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to the height of 4.0 m. Compute the force necessary to keep the door closed