Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 13: Exercise (Conceptual Questions)

If $\mathrm{tan\theta }=\frac{1}{\sqrt{5}}$ and $\mathrm{\theta }$ lies in the first quadrant, the value of $\cos \theta$ is:

Frequency $\mathrm{f}$ of a simple pendulum depends on its length $\mathcal{l}$ and acceleration $\mathrm{g}$ due to gravity according to the following equation $\mathrm{f}=\frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{g}}{\mathcal{l}}}$. Graph between which of the following quantities is a straight line?

Two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ lie in a plane, another vector $\overrightarrow{\mathrm{C}}$ lies outside the plane, then the resultant of these three vectors i.e., $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{C}}$

The minimum number of vectors in different planes which can be added to give zero resultant is

Which of the following sets of concurrent forces may be in equilibrium?

If a unit vector is represented by $0.5\hat{\mathrm{i}}+0.8\hat{\mathrm{j}}+c\hat{\mathrm{k}}$ then the value of $c$ is:

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces:

In an orbital motion, the angular momentum vector is