A circular plate of diameter ' $a$ ' is kept in contact with a square plate of side $a$ as shown. The density of the material and the thickness are same everywhere. The centre of mass of composite system will be ...........
Inside the circular plate
Inside the square plate
At the point of contact
Outside the system
A uniform circular disc of radius $a$ is taken. A circular portion of radius $b$ has been removed from it as shown in the figure. If the centre of hole is at a distance $c$ from the centre of the disc, the distance $x_2$ of the centre of mass of the remaining part from the initial centre of mass $O$ is given by
A man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friction. Which of the following figures depicts the motion of the centre of mass of the entire system (man, the ball and the box)?
$A$ point mass $m_A$ is connected to a point mass $m_B$ by a massless rod of length $l$ as shown in the figure. It is observed that the ratio of the moment of inertia of the system about the two axes $BB$ and $AA$, which is parallel to each other and perpendicular to the rod is $\frac{{{I_{BB}}}}{{{I_{AA}}}}=3$. The distance of the centre of mass of the system from the mass $A$ is
A square shaped hole of side $l=\frac{a}{2}$ is carved out at a distance $d =\frac{ a }{2}$ from the centre $'O'$ of a uniform circular disk of radius $a$. If the distance of the centre of mass of the remaining portion from $O$ is $-\frac{a}{X},$ value of $X$ (to the nearest integer) is.......
On a horizontal frictionless frozen lake, a girl $36 \,kg$ and a box $9 \,kg$ are connected to each other by means of a rope. Initially, they are $20 \,m$ apart. The girl exerts a horizontal force on the box, pulling it towards her. How far has the girl travelled when she meets the box?