Question

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 the time $t=0$ , $A$ is given a tangential acceleration of magnitude $a=\frac{32 v^{2}}{25 \pi R}$ in the same direction of the initial velocity. Then which of the following is correct

• A. The time-lapse for the two bodies to collide is $\frac{6 \pi R}{5 V}$
• B. The angle covered by A is $\frac{9 \pi }{4}$
• C. Angular velocity of A is $\frac{11 V}{5 R}$
• D. Radial acceleration of A is $\frac{289 V^{2}}{5 R}$

Answer 1

Answer: (B)

As when they
Collide $\frac{1}{2}\left(\frac{32 \, v^{2}}{25 \, \pi R}\right)t^{2}=\pi R$
$t=\frac{5 \pi R}{4 V}$
Angle covered by A
$\theta =\pi +\frac{v t}{R}$
$\theta =\frac{9 \pi }{4}$