Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 4: Exercise-4

Figure shows a uniform square plate from which four identical squares at the corners will be removed.
(i) Where is the centre of mass of the plate originally.
 

Figure shows a uniform square plate from which four identical squares at the corners will be removed.
(ii) Where is C.M. after square $1$ is removed.
 

Figure shows a uniform square plate from which four identical squares at the corners will be removed.

(iii) Where is C.M. after squares $1$ and $2$ removed.

Give Answers in terms of quadrants and axes.

Figure shows a uniform square plate from which four identical squares at the corners will be removed.

(iv) Where is C.M. after squares $1$ and $3$ are removed.

Give Answers in terms of quadrants and axes.

Figure shows a uniform square plate from which four identical squares at the corners will be removed.
.
(v) Where is C.M. after squares $1,2$ and $3$ are removed.

Give Answers in terms of quadrants and axes.

Figure shows a uniform square plate from which four identical squares at the corners will be removed.
(vi) Where is C.M. after all the four squares are removed.
Give Answers in terms of quadrants and axes.

A bullet of mass $M$ is fired with a velocity $50 \mathrm{m}/\mathrm{s}$ at an angle $\theta$ with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass $3M$ suspended by a massless string of length $\frac{10}{3}$ metres and gets embedded in the bob, after the collision the string moves through an angle of $120°$. Find :

(ii) the vertical and horizontal coordinates of the initial position of the bob with respect to the point of firing of the bullet. (Take $g=10 \mathrm{m}/{\mathrm{s}}^2$).

Two blocks of masses $m_1$ and $m_2$ are connected by a massless pulley $A$, slides along the smooth sides of a rectangular wedge of mass $m$, which rests on a smooth horizontal plane. Find the distance covered by the wedge on the horizontal plane till the mass $m_1$ is lowered by the vertical distance $h$.