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 :