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

If $\vec F$ is the force acting on a particle having position vector $\vec r$ and $\vec \tau $ be the torque of this force about the origin, then

The force $7\hat i + 3\hat j - 5\hat k$ acts on a particle whose position vector is $\hat i - \hat j + \hat k$. What is the torque of a given force about the origin ?

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity $\omega $ . Then the force exerted by the liquid at this other end is

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

A man of $50\, kg$ mass is standing in a gravity free space at a heigth of $10\,m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed of $2\,m/s$. When the stone reaches the floor, the distance of the man above the floor will be ........ $m.$