The pulley arrangement of figure are identical. The mass of the rope i

1.	The pulley arrangement of figure are identical. The mass of the rope is negligible. In (a) mass m is lifted up by attaching a mass (2m) to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force F = 2 mg. In which case, the acceleration of m is more?
Answer» Case (a) : a = \(\frac{2m - m} {2m + m} g\) = a = \(\frac{g}{3}\) Case (b): FBD of mass m ma’ = T – mg ma’ = 2 mg – mg ⇒ ma’ = mg a’ = g So in case (b) acceleration of m is more.

The pulley arrangement of figure are identical. The mass of the rope is negligible. In (a) mass m is lifted up by attaching a mass (2m) to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force F = 2 mg. In which case, the acceleration of m is more?

Answer»

Case (a) :

a = \(\frac{2m - m} {2m + m} g\) = a = \(\frac{g}{3}\)

Case (b):

FBD of mass m

ma’ = T – mg

ma’ = 2 mg – mg

⇒ ma’ = mg

a’ = g

So in case (b) acceleration of m is more.