A uniform rod of mass ‘m’ and length ‘ $ℓ$ ’ is held horizontally by two vertical strings ‘A’ and ‘B’ of negligible mass and a small block of mass ‘m’ is also placed on the top of the rod as shown in the figure. Then which of the following is/are correct.

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The tension in the string ‘A’ immediately after the string ‘B’ is cut, it $\frac{4}{7} m g$ .

The acceleration of centre of mass of the rod and the block immediately after the string ‘B’ is cut, is $\frac{5}{7} g$ .

The tension in the sting ‘A’ immediately after the string ‘B’ is cut, is $\frac{2}{7} m g$ .

The acceleration of centre of mass of the rod immediately after the string ‘B’ is cut, is $\frac{3}{7} g$ .

answer is A, C, D.

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Detailed Solution

Just after cutting the string B, block loses the contact with the rod.
Taking torque about P.
$m g \frac{ℓ}{4} = (\frac{m ℓ^{2}}{12} + \frac{m ℓ^{2}}{16}) α α = \frac{12}{7} \frac{g}{ℓ}, a_{c m} = \frac{ℓ}{4} α = \frac{3}{7} g m g - T = m a_{c m} T = \frac{4}{7} m g$