Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 1: BEGINNER'S BOX - 1

A machine gun fires a bullet of mass $50 \mathrm{gm}$ with a velocity $1000 \mathrm{m} {\mathrm{s}}^{-1}$. If the average force acting on the gun is $200 \mathrm{N}$, then find out the maximum number of bullets fired per minute.

A force of $10 \mathrm{N}$ acts on a body for $3 \mathrm{\mu } \mathrm{s}$. If the mass of the body is $5 \mathrm{g}$, calculate the impulse and the change in velocity.

The magnitude of the force (in newton) acting on a body varies with time $t$ (in microsecond) as shown in the figure $AB$, $BC$ and $CD$ are straight line segments. Find the magnitude of the total impulse of the force (in $\mathrm{N}-\mathrm{s}$) on the body from $t=4 \mathrm{\mu s}$ to $t=16 \mathrm{\mu s}$.

What are the coordinates of the centre of mass of the three particles system shown in the figure? 

Four particles of masses $m, 2m, 3m, 4m$ are placed at the corners of a square of side $a$ as shown in figure. Find out the coordinates of the centre of mass.

A rigid body consists of a $3 \mathrm{kg}$ mass connected to a $2 \mathrm{kg}$ mass by a massless rod. The $3 \mathrm{kg}$ mass is located at $\overrightarrow{r}=(2\hat{\mathrm{i}} +5\hat{\mathrm{j}}) \mathrm{m}$ and the $2 \mathrm{kg}$ mass at ${\overrightarrow{r}}_2=(4\hat{\mathrm{i}} + 2\hat{\mathrm{j}}) \mathrm{m}$. Find the position and coordinates of the centre of mass. 

Figure shows a uniform square plate from which one or more of the four identical squares at the corners will be removed.
  
(a) Where is the centre of mass of the plate originally?
(b) Where is the C.M. after square $1$ is removed?
(c) Where is the C.M. after squares $1$ and $2$ removed?
(d) Where is the C.M. after squares $1$ and $3$ are removed?
(e) Where is the C.M. after squares $1, 2$ and $3$ are removed?
(f) Where is the C.M. after all the four squares are removed?
Give your answers in terms of quadrants and axis.
 

Find the centre of mass of a uniform disc of radius $a$ from which a circular section of radius $b$ has been removed. The centre of the hole is at a distance $c$ from the centre of the disc.