System of Parti...

A ladder is leaned against a smooth wall and allowed to slip on a frictionless floor. Which figure represents trace of its COM ?

A body has its center of mass at the origin. The x-axis coordinates of the particles :

Two balls of equal masses are projected upward simultaneously, one from the ground with speed $50m/s$ and other from a $40m$ high tower with initial speed $30m/s$. Find the maximum height attained by their centre of mass.

A particle of mass m is moving in horizontal circle of radius $r$ with uniform speed $v$. When it  moves from one point to a diametrically opposite point its 

A pulley is hinged at the centre and a massless thread is wrapped around it. The thread is pulled with a constant force F starting from rest. As the time increases:

A particle of mass $m$ strikes a wall with a velocity $v$ making an angle $\theta$ with the wall and rebounds.The change in momentum of the particle will be :

Two identical rods are joined to form the shape of X. the smaller angle between rods is $\theta$. The moment of inertia of the system about an axis passing through the point of intersection of the rod and perpendicular to their plane is

The diameter of a solid disc is $0.5$ m and its mass is $16$ Kg. What torque will increase its angular velocity from zero to $120$ rotation/minute in $8$ seconds ?

A flywheel of moment of inertia $0.4\,Kg/m^2$ and radius $0.2  m$ is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of $10  N$ then its angular velocity after $4  s$ will be

Two particles of mass 1 kg and 3 kg move towards each other under mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is $\displaystyle{2 ms^{-1}}$ their centre of mass has a velocity of $\displaystyle{0.5 ms^{-1}}$ and when their velocity of approach become $\displaystyle{3 ms^{-1}}$, the velocity of their centre of mass is $\displaystyle{0.75 ms^{-1}}$. Then,