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+### Statement
+
+$2.1.55.$ [Insert the problem statement]
+
+### Solution
+
+### Statement
+
+$2.1.55.$ Two small spheres, each of mass $m$, connected by a thread of length $l$, are moving with a velocity $v$ on a horizontal table in a direction perpendicular to the connecting thread (the thread is taut). The middle of the thread hits a nail. What is the tension force of the thread immediately after this?
+
+### Solution
+
+![Forces acting on the system|590x284, 47%](../../img/2.1.55/draw.png)
+
+Since the thread is taut:
+
+$$
+T_1 = T_2 = T
+$$
+
+As soon as the thread hits the nail, both bodies continue to move with velocity $v$ along a new trajectory with radius $r=\\frac{l}{2}$:
+
+$$
+T=ma_n
+$$
+
+$$
+T=m\\frac{v^2}{\\frac{l}{2}}
+$$
+
+We obtain the tension force of the thread immediately after this:
+
+$$
+\\boxed{T = \\frac{2m v^2}{l}}
+$$
+
+#### Answer
+
+$$
+T = \\frac{2m v^2}{l}
+$$
+
+#### Answer
+
+[Insert a concise answer or boxed result]