JEE Main & Advanced Physics Two Dimensional Motion Question Bank Self Evaluation Test - Motion in a Plane

Two particles A and B separated by a distance 2R are moving counter clockwise along the same circular path of radius R each with uniform speed v. At time \[t=0\], A is given a tangential acceleration of magnitude \[\alpha =\frac{\text{77}{{\text{v}}^{2}}}{25\pi \text{R}}\] then

A) the time lapse for the two bodies to collide is \[\frac{6\pi \text{R}}{5\text{v}}\]

B) the angle covered by A is 11\[\pi \]/6

C) angular velocity of A is \[\frac{11\text{v}}{5\text{R}}\]

D) radial acceleration of A is \[\text{289 }{{\text{v}}^{\text{2}}}\text{/5R}\]

Correct Answer: B

Solution :

[b] As when they collide \[vt+\frac{1}{2}\left( \frac{77{{v}^{2}}}{25\pi R} \right){{t}^{2}}-\pi R=vt\]

\[\therefore \,\,\text{t}=\frac{\text{5}\pi \text{R}}{\text{6v}}\]

Now, angle covered by \[\text{A}=\pi +\frac{\text{vt}}{\text{R}}\]

Put t, \[\therefore \text{ angle covered by A=}\frac{11\pi }{6}\]