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Three particles each of mass m can slide...

Three particles each of mass m can slide on fixed frictionless horizontal circular tracks in the same horizontal plane as shown in the figure. The coefficient of restitution being `e = 0.5`. Assuming that `m_(2)` and `m_(3)` are at rest initially and lie along a radial line before impact and the string is initially unstretched, then maximum extension in spring in subsequent motion

A

`1/4 v_( 0)sqrt((m)/(5K))`

B

`3/4 v_(0)sqrt((m)/(5K))`

C

`1/3 v_(0)sqrt((m)/(5K))`

D

`1/8 v_(0)sqrt((m)/(5K))`

Text Solution

Verified by Experts

The correct Answer is:
B
By the conservation of linear momentum between `m_(1)` and `m_(2)` and by using coefficient of restitution velocity `m_(2)` just after collision `(3v_(0))/(4)`.
After the collision, the maximum extension in the spring occurs when angular velocity of `m_(2)` and `m_(3)` about O become same. Now by conservation of angular momentum about .O. and energy conservation
Velocity of `m_(2)=2 R omega=3/5 v_(0)`
Velocity of `m_(3)=R omega = (3)/(10)v_(0)` and `Deltax` maximum `=3/4 v_(0) sqrt((m)/(5K))`
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