Concepts Of Physics MCQ Edition [Volume 1]PhysicsCircular Motion
A table featuring a smooth horizontal surface is situated in a cabin that travels in a circle of large radius R with angular velocity , as shown in the figure. A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected by a string going over the pulley. Initially, the masses are held by a person with the strings lying along the outward radius, and then the system i
Options
- A^2 R 3 , 4 3 m ^2 R
- B^2 R 2 , 4 3 m ^2 R
- C^2 R 3 , 2 3 m ^2 R
- D2 ^2 R 3 , 2 3 m ^2 R
Correct answer
A. ^2 R 3 , 4 3 m ^2 R
Step-by-step solution
In the rotating frame of the cabin, each mass experiences a centrifugal force directed radially outwards. Since the radius R is large, the centrifugal force on a mass M can be approximated as M ^2 R . Let the two masses be m₁ = 2m and m₂ = m . Both masses are placed such that the strings lie along the outward radius, meaning the centrifugal force acts outwards (away from the pulley) on both masses, while the tension T acts inwards (towards the pulley). The centrifugal forces on the masses are: For the 2m mass: F₁ =