The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\, mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere) :-
$\frac{1}{6}$
$\frac{7}{6}$
$1$
$\frac{1}{2}$
The centre of mass of a body
In a bicycle the radius of rear wheel is twice the radius of front wheel. If $r_F$ and $r_r$ are the radius, $v_F$ and $v_r$ are the speeds of top most points of wheel, then
The centre of mass of two particles lies
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?
A uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega $ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is