System of Parti...

Four identical rods, each of mass $$m$$ and length $$l$$, are joined to form a rigid square frame. The frame lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its moment of inertia about :

Find the acceleration of the point $$K$$.

Two masses $$\displaystyle{M_1}$$ and $$\displaystyle{M_2}$$ are connected with each other with the help of a massless spring of spring-constant $$k$$. Mass $$\displaystyle{M_1}$$ is in contact with a wall and the system is at rest on the frictionless floor. $$\displaystyle{M_2}$$ is displaced by distance $$x$$ to compress the spring and released. The velocity of COM (centre of mass) of the system when $$\displaystyle{M_1}$$ is detached from wall is :

A particle of rest mass $$m_0$$ is moving with speed $$c/2$$. What is its momentum? 

A cracker is thrown into air with a velocity of 10 m/s at an angle of 45$$^o$$ with the vertical. When it is at a height of 0.5 m from the ground, it explodes into a number of pieces which follow different parabolic paths. What is the velocity of centre of mass, when it is at a height of 1 m from the ground? $$(g = 10 m/s^2)$$

The distance of the centre of mass of the T-shaped plate from O is

A particle of mass $$m$$ is acted on by two forces of equal magnitude $$F$$ maintaining their orientation relative to the velocity $$v$$ as shown in figure. The momentum of the particle :

Two particles are shown in figure. At $$t = 0$$, a constant force $$F = 6$$N starts acting on the 3 kg mass. Find the velocity of the centre of mass of these particles at $$t = 5 s$$.

The moment of inertia of a solid sphere about an axis passing through the centre of gravity is $$2/5 MR^{2}$$, then its radius of gyration about a parallel axis at a distance $$2R$$ from first axis is 

Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks in the centre of mass frame after the kick are, respectively :