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=(32 v2/25 π R) in the same direction of the initial velocity. Then which of the following is correct

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=(32 v2/25 π 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 (6 π R/5 V) (B) The angle covered by A is (9 π /4) (C) Angular velocity of A is (11 V/5 R) (D) Radial acceleration of A is (289 V2/5 R)

Tardigrade Admin · Accepted Answer

As when they Collide (1/2)((32 v2/25 π R))t2=π R t=(5 π R/4 V) Angle covered by A θ =π +(v t/R) θ =(9 π /4)

The time-lapse for the two bodies to collide is $\frac{6 π R}{5 V}$

The angle covered by A is $\frac{9 π}{4}$

Angular velocity of A is $\frac{11 V}{5 R}$

Radial acceleration of A is $\frac{289 V ^{2}}{5 R}$

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

The time-lapse for the two bodies to collide is 5V6πR​

The angle covered by A is 49π​

Angular velocity of A is 5R11V​

Radial acceleration of A is 5R289V2​

As when they Collide 21​(25πR32v2​)t2=πR t=4V5πR​ Angle covered by A θ=π+Rvt​ θ=49π​

The time-lapse for the two bodies to collide is $\frac{6 π R}{5 V}$

The angle covered by A is $\frac{9 π}{4}$

Angular velocity of A is $\frac{11 V}{5 R}$

Radial acceleration of A is $\frac{289 V ^{2}}{5 R}$

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