Embibe Experts Solutions for Exercise 2: EXERCISE 6.2

From a square sheet of uniform density, a portion is removed shown as shaded region in the figure. Find the centre of mass of the remaining portion if the side of the square is $a$.

A uniform circular disc of radius '$a$' is taken. A circular portion of radius '$b$' has been removed from it as shown in 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 $O$ is given by:

Find the velocity of centre of mass if the triangle formed is equilateral.

If the net force acting on the system of particles is zero, then which of the following may vary?

A mortar fires a shell of mass M which explodes into two pieces of mass $\frac{M}{5}$ and $\frac{4M}{5}$ at the top of the trajectory. The smaller mass falls very close to the mortar. In the same time the bigger piece lands a distance $D$ from the mortar. The shell would have launched at a distance $R$ from the mortar if there was no explosion. The value of $D$ is (Neglect the air resistance):

Consider a semicircular ring of radius $R$. Its linear mass density varies as $\lambda ={\lambda }_0\sin \theta$. Locate its centre of mass.

A particle of mass $2m$ is projected at an angle of $45°$ with horizontal with a velocity of $20\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$. After $1 \mathrm{s}$ explosion takes place and the particle is broken into two equal pieces. As a result of the explosion, one part comes to rest. The maximum height attained by the other part is (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)