Two objects of mass $10\,kg$ and $20\,kg$ respectively are connected to the two ends of a rigid rod of length $10\,m$ with negligible mass. The distance of the center of mass of the system from the $10\,kg$ mass is :

In the figure shown find out the distance of centre of mass of a system of a uniform circular plate of radius $3R$ from $O$ in which a hole of radius $R$ is cut whose centre is at $2R$ distance from centre of large circular plate

There are some passengers inside $a$ stationary railway compartment. The track is frictionless. The centre of mass of the compartment itself (without the passengers) is $C_1$, while the centre of mass of the 'compartment plus passengers' system is $C_2$. If the passengers move about inside the compartment along the track.

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

Define the position vector of centre of mass.

Consider the following statements

Assertion $(A)$ : $A$ cyclist always bends inwards while negotiating a curve

Reason $(R)$ : By bending he lowers his centre of gravity Of these statements,