Q 11-05-018NEETJEE MainEAMCET 2013 (Engineering)Hard
A block of mass $2.9$ kg is suspended from a string of length $50$ cm and is at rest. Another block of mass $100$ g, which is moving with a speed of $150$ m/s, strikes and sticks to the first block. Subsequently, when the string makes an angle of $60°$ with the vertical, the tension in the string will be ($g = 10\ \text{m s}^{-2}$)
Answer: (B) $135$ N
Collision (momentum conserved): $0.1 \times 150 = 3.0\,v \Rightarrow v = 5$ m/s.
Speed at $60°$ (height gained $l(1 - \cos 60°) = 0.25$ m):
$$v'^2 = 25 - 2(10)(0.25) = 20$$
Radial equation at $60°$:
$$T = mg\cos 60° + \frac{mv'^2}{l} = 3(10)(0.5) + \frac{3 \times 20}{0.5} = 15 + 120 = 135\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics