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,