A string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to ceiling. Centre of mass falls down as the disc unwinds the string. The tension in the string is
$Mg/6$
$Mg/3$
$Mg/2$
$2Mg/3$
Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same time $t$. The ratio of the angular speeds of the first to the second car is
A hoop of radius $r$ and mass $m$ rotating with an angular velocity ${\omega _0}$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity $\omega $. The force exerted by the liquid at the other end is
Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when velocity of $A$ is $v$ and that of $B$ is $2v$, the velocity of centre of mass of the system :
$A$ car travelling on a smooth road passes through $a$ curved portion of the road in form of an arc of circle of radius $10 m$. If the mass of car is $500\, kg$, the reaction on car at lowest point $P$ where its speed is $20 m/s$ is ......... $kN$.