Two identical small balls, each of mass `m`, are connected by a massless and inextensible string of length `l` and placed on a smooth horizontal `xy` plane. An external agent pulling the string from its mid-point along `y`-axis with velocity `v_(0)` as shown in Fig. When the separation between the two balls reduces to `l//2` then the speed of each ball will be

Options

A. `2v_(0)`
B. `v_(0)`
C. `(v_(0))/2`
D. none of the above

Answer

B

Explanation

Using conservation of angular momentum about the midpoint we can fnd the velocity of each ball relative to the midpoint i.e. `v'=v_0`

Resultant velocity of ball `=`velocity of mid point `+`velocity of ball w.r.t midpoint
or `v=sqrt(v_(0)^(2)+v_(0)^(2)+2v_(0)^(2)cos120^@)=v_(0)`