B M Sharma Solutions for Chapter: Vectors, Exercise 48: Archives

A small particle of mass $m$ is projected at an angle $\mathrm{\theta }$ with the $x$-axis with an initial velocity $v_0$ in the $x-y$ plane as shown in the figure. At a time $t<\frac{v_0\mathrm{sin\theta }}{g},$ the angular momentum of the particle is

A particle is moving with velocity $\overrightarrow{v}=K(y\mathrm{i}+x\mathrm{j}),$ where $K$ is a constant. The general equation for its path is

A projectile is given an initial velocity of $\left(\hat{i}+2\hat{j}\right)m/s$ where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g=10 m/s^2,$ the equation of its trajectory is

Three vectors $P, Q$ and $\overrightarrow{R}$ are shown in the figure. Let $S$ be any point on the vector $\overrightarrow{R}.$ The distance between the points $P$ and $S$ is $b\left|\overrightarrow{R}\right|.$ The general relation among vectors $\overrightarrow{P},\overrightarrow{Q}$ and $\overrightarrow{S}$ is:

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are defined as $\overrightarrow{A}=a\hat{\mathrm{i}}$ and $\overrightarrow{B}=a\left(\mathrm{cos\omega t}\hat{\mathrm{i}}+\mathrm{sin\omega t}\hat{\mathrm{j}}\right)$ where $a$ is a constant and $\omega =\frac{\pi }{6} \mathrm{rad} {\mathrm{s}}^{-1}.$ If $|\overrightarrow{A}+\overrightarrow{B}|=\sqrt{3}|\overrightarrow{A}-\overrightarrow{B}|$ at time $t=\tau$ for the first time, the value of $\tau ,$ in seconds is ______.