A tunnel is dug in the earth across one of its diameter. Two masses m and 2m are dropped from the two ends of the tunnel . The masses collide and stick each other. They perform SHM, the amplitude of which is :
Answer & explanation
Correct answer: option 3
\(2 mu - mu = 3 mv\)
\(\Rightarrow v = \frac{u}{3}\)
\(\frac{1}{2}mu^2 = \frac{3GMm}{2R} - \frac{GMm}{R} \)
\(u = \sqrt{\frac{Gm}{R}}\)
\(\Delta U(r) = \frac{GM (3m)}{2R^3}A^2\)
\(\Delta U(r) = \frac{1}{2} 3m.v^2\)
\(\Rightarrow \frac{GM}{2R^3}A^2 = \frac{1}{2} \frac{1}{9} \frac{GM}{R}\)
\(\frac{A^2}{R^2} = \frac{1}{9}\)
\(\Rightarrow A = \frac{R}{3}\)