Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices $A, B, C$ and $D$ of a square of side $1\, m$. The coordinates of centre of mass of the particles are
$(0.3 \,m, 0.5 \,m)$
$(0.5 \,m, 0.3 \,m)$
$(0.2 \,m, 0.2 \,m)$
$(0.3 \,m, 0.2 \,m)$
Four particles of masses $m_1 = 2m, m_2 = 4m, m_3 = m$ and $m_4$ are placed at four corners of a square. What should be the value of $m_4$ so that the centres of mass of all the four particles are exactly at the centre of the square ?
If a solid sphere is rolling the ratio of its rotational energy to the total kinetic energy is given by
In the given figure linear acceleration of solid cylinder of mass $m_2$ is $a_2$ . Then angular acceleration $\alpha_2$ is (given that there is no slipping)
$A$ bob of mass $m$ is attached to a string whose other end is tied to a light vertical rod as shown in figure. The bob is swinging in horizontal plane with constant angular speed $\omega$. The vertical rod is supported on a block of mass $M$ which is placed on a rough surface. What is minimum friction coefficient between ground and block for which block does not slip ?
Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is : (mass of the ring $= m,$ radius $= r$ )