Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 1: KEAM 2018

Four particles of masses ${\mathrm{m}}_1=1\mathrm{kg},{\mathrm{m}}_2=2\mathrm{kg},{\mathrm{m}}_3=1\mathrm{kg}$ and ${\mathrm{m}}_4$ are placed at the four corners of a square. The mass ${\mathrm{m}}_4$ required, so that the centre of mass of all the four particles is exactly at the centre of the square is

Two particles of mass $m$ and $2m$ have their position vectors as a function of time as $r_1\left(t\right)=t \hat{\mathrm{i}}-t^3\widehat{ \mathrm{j}}+2t^2 \hat{\mathrm{k}}$ and $r_1\left(t\right)=t \hat{\mathrm{i}}-t^3 \hat{\mathrm{j}}-t^2 \hat{\mathrm{k}}$ respectively (where $t$ is the time). Which one of the following graphs represents the path of the centre of mass?

A block of mass $\mathrm{1 }kg$ is free to move along the $X$ -axis. It is at rest and from time $t=0$ onwards it is subjected to a time-dependent force $F\left(t\right)$ in the $x$ -direction. The force $F\left(t\right)$ varies with $t$ as shown in figure. The kinetic energy of the block at $t=4$ s is