Circular Motion

Q. Two satellites, of masses m and 2 m, are on the same circular orbit around earth. If the velocity of the lighter satellite is $v_o$ , what is the velocity of the heavier satellite?

1. $\frac{1}{2}{v}_o$
2. $v_o$
3. $2v_o$
4. $\frac{1}{4}{v}_o$

Q. Two particles, P and Q are initially at two ends of a circular arc which subtends an angle 120${}^o$ at the arc-center. The radius of the arc is r. The particles P and Q are moving along the arc towards each other with constant tangential velocities of $V_P$ and $V_Q$ respectively. The distance travelled by the particle P when it meets the particle Q is

1. $\frac{2\pi }{3}\frac{r(V_P+V_Q)}{V_P}$
2. $\frac{2\pi }{3}\frac{r(V_P+V_Q)}{V_Q}$
3. $\frac{2\pi }{3}\frac{r{V}_P}{(V_P+V_Q)}$
4. $\frac{2\pi }{3}\frac{r{V}_Q}{(V_P+V_Q)}$

Q. A homogeneous circular disc of radius r and weight W hangs in a vertical plane from a point O at its circumference. Find the period for small angles of swing in the plane of the disc.

1. $2\pi \sqrt{\frac{r}{g}}$
2. $2\pi \sqrt{\frac{3r}{2g}}$
3. $\pi \sqrt{\frac{3r}{2g}}$
4. $2\pi \sqrt{\frac{r}{3g}}$

Q. A mass 'M' is suspended from a ceiling through a string of length 'L'. This mass moves in a circle of horizontal radius 'r'. at constant speed such that it is a conical pendulum. The tension in the string will-be

1. $mgL/\left(22\sqrt{L^2-r^2}\right)$
2. $mgL/\sqrt{L^2}$
3. $mgL/\sqrt{r^2}$
4. $mgL/\left(\sqrt{L^2-r^2}\right)$

Q. A mass attached to a string is swung in a circular path with a uniform angular velocity about the horizontal plane, as shown. Seen directly from above, which path would the mass most closely follow if the string breaks suddenly at T?

1. P
2. Q
3. R
4. S