System of Parti...

A uniform cube of side a and mass m rests on a rough horizontal surface. A horizontal force F is applied normal to face at a point that is directly above the centre of the face at a height $$\cfrac{\alpha}{4}$$ above the centre. The minimum value of F for which the cube begins to topple above an edge without sliding is:

A solid cylinder of mass $$M$$ and radius $$R$$ is rolling without slipping on a horizontal plane with a speed $$v$$. it the rolls up an inclined plane of inclination $$\theta$$ to a maximum height given by

The velocity of centre of mass of the system as shown in the figure.

The end A of a ladder AP of length 5 m, kept inclined to a vertical wall is slipping over a horizontal surface, when A is at a distance of 3 m from the wall. If velocity of centre of mass at this moment is $$1.25 m/s$$ then velocity of the lowest point A of the ladder at tis instant is :-

A system of binary stars of masses $$m_{A}$$ and $$m_{B}$$ are moving in circular orbits of radii $$r_{A}$$ and $$r_{B}$$ respectively. If $$T_{A}$$ and $$T_{B}$$ are the time periods of masses $$m_{A}$$ and $$m_{B}$$ respectively, then

if a force$$ 10\hat { i } +15\hat { j } +25\hat { K }$$ acts on a system and gives an acceleration $$2\hat { i } +3\hat { j } -5\hat { K } $$ to the centre of mass of the system, the mass of the system is :

Three man $$  A, B \& C  $$ of mass $$  40 \mathrm{kg}, 50 \mathrm{kg} \& 60 \mathrm{kg}  $$ are standing on a plank of mass $$90  \mathrm{kg}  $$ .which is kept on a smooth horizontal plane. If $$ \mathrm{A} \& \mathrm{C}  $$ exchange their positions then mass $$ \mathrm{B}  $$ will shift

A rod of moment of inertia I and length L is suspended from a fixed end and given small oscillations about the point of suspension , the restoring torque is found to be -(mgL/2) $$sin\theta $$ What will be the angular equation of motion of the SHM

Three identical rods, each of length I, are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is

Force F=300 N acting vertically upward at x=2 m, y=2 m. The magnitude of moment of force about origin is