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 disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v,$ the height to which the disc will rise will be

Three thin metal rods, each of mass $M$ and length $L$ are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is

A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom

Radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is

Two particles whose masses are $10\,kg$ and $30\,kg$ and their position vectors are $\hat i +\hat j+ \hat k$ and $-\hat i -\hat j -\hat k$ respectively would have the centre of mass at