A spring can be used to determine the mass m of an object in two ways : (i) by measuring the extension in the spring due to the object; and (ii) by measuring the oscillation period for the given mass. Which of these methods can be used in a space-station orbiting Earth ?
Both
Only the extension method
Only the oscillation method
Neither
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC NDA-1 – 2015
Method (i) involves measuring the extension of a spring caused by the weight of the object (F = mg, where F is the force causing extension, m is mass, and g is acceleration due to gravity). In a space station orbiting Earth, objects are in a state of apparent weightlessness because they are in free fall. The effect of gravity is effectively absent for this type of measurement, so there would be no significant extension of the spring due to the object’s mass in the absence of gravitational force acting downwards. Method (ii) involves measuring the oscillation period of a mass attached to a spring. The period of oscillation (T) of a simple harmonic oscillator like a mass-spring system is given by T = 2π√(m/k), where m is the mass and k is the spring constant. This formula depends on mass (m) and spring constant (k), but not on gravity (g). Therefore, the oscillation method can be used to determine mass in a weightless environment like an orbiting space station.
Measuring extension relies on weight (force due to gravity), which is effectively zero in orbit. Measuring oscillation period relies on inertial mass and spring constant, which are unaffected by gravity.