B M Sharma Solutions for Chapter: Gravitation, Exercise 1: CONCEPT APPLICATION EXERCISE

A planet sweeps areas $A$ and $2 A$ during a small time intervals $\Delta t_1$ and $\Delta t_2$ respectively. Find $\frac{\Delta t_1}{\Delta t_2}$.

Find the ratio of time period of revolution of the planets $1$ and $2$.

If a planet moving in a circular path having time period of revolution $T$ is suddenly stopped, after what time it will collapse onto the sun?

A particle of mass $m$ moves along a straight line with constant velocity ${\overrightarrow{v}}_0$ in the $x$ direction at a distance $b$ from the $x$ axis (figure).

(a) Does the particle possess any angular momentum about the origin?
(b) Explain why the amount of its angular momentum should change or should stay constant.
(c) Show that Kepler's second law is satisfied by showing that the two shaded triangles in the figure have the same area when $t_{\left(D\right)}-t_{\left(\mathrm{C}\right)}=t_{\left(\mathrm{B}\right)}-t_{\left(\mathrm{A}\right)}$.