Question

Two bodies A and B are moving with same constant speed $v$ in clockwise direction in a horizontal circle of radius $R$ and are initially diagonally opposite. The particle B now achieves a tangential acceleration $a$ $m/s^2.$ Then:

• A. they collide after time $\sqrt{\frac{\pi R}{a}}$
• B. they collide after time $\sqrt{\frac{2\pi R}{a}}$
• C. relative velocity just before collision is$\sqrt{\pi aR}$
• D. relative velocity just before collision is $\sqrt{2\pi aR}$

Answer 1

Answer: (B), (D)

relative velocity just before collision is $\sqrt{2\pi aR}$
they collide after time $\sqrt{\frac{2\pi R}{a}}$

In order to collide,

$\pi R+$ Distance travelled by A = Distance travelled by B
or, $\pi R+vt=vt+\frac{1}{2}a{t}^2$
or, $t=\sqrt{\frac{2\pi R}{a}}$
Relative velocity just before collission:

$V_{BA}=V_B-V_A=0+a.t=a\times \sqrt{\frac{2\pi R}{a}}=\sqrt{2\pi aR}.$