The centre of mass of two masses $m$ and $m'$ moves by distance $\frac {x}{5}$ when mass $m$ is moved by distance $x$ and $m'$ is kept fixed. The ratio $\frac {m'}{m}$ is

A ring of radius $4a$ is rigidly fixed in vertical position on a table. A small disc of mass $m$ and radius $a$ is released as shown in the fig. When the disc rolls down, without slipping, to the lowest point of the ring, then its speed will be

Two uniform thin identical rods $AB$ and $CD$ each of mass $M$ and length $L$ are joined so as to form a cross as shown. The moment of inertia of the cross about a bisector line $EF$ is (Line $EF$ is perpendicular to $ABCD$ plane)

A thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $\omega$. If two objects each of mass $m$ be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity

A balloon of mass $M$ with a light rope and monkey of mass $m$ are at rest in mid air. If the monkey climbs up the rope and reaches the top of the rope, the distance by which the balloon descends will be(Total length of the rope is $L$ )

In the following figure, a body of mass $m$ is tied at one end of a light string and this string and this string is wrapped around the solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$ the system starts moving. If the friction is negligible, angular velocity at time $t$ would be