Two astronauts each have a mass of 75.0 kg are connected by a 10.0 m long rope of negligible mass. They are isolated in space and orbit around common centre of mass with a speed of 5.0 m/s as shown in figure. Then,

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Tension in the string will be 375 N

tension in the string will be 1500 N

acceleration of astronaut will be 20 ${m/s}^{2}$

acceleration of astronaut will be 5 ${m/s}^{2}$

answer is A, C.

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Detailed Solution

By symmetry, velocity of each is 5 m/s
$T = \frac{m v^{2}}{R} = \frac{75 \times 25}{5} = 375 N$
Acceleration $\frac{v^{2}}{R} = \frac{25}{5} {= 5 m/s}^{2}$

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