Question

The pulley arrangements shown in the figure are identical, the mass of the rope is negligible. In case (I) the mass m is lifted by attaching a mass $2m$ to the other end of rope. and in case (II), with a constant downward force $F=2mg$, where $g$ is acceleration due to gravity. The acceleration of mass m in case (I) is :

• A. zero
• B. more than that in case II
• C. less than that in case II
• D. equal to that in case II

Answer 1

Answer: (C)

less than that in case II

Case 1: $a=g(\frac{m_1-m_2}{m_1+m_2})$
Case 2: F-T $=0$ and $T=2mg$
also T-mg $=m{a}^1$ Finally $a<a^1$

Case 1: Tensin in the string will $2mg-2ma$,where $a$ is the acceleration of masses.
Case 2: Tension in string is $2mg$.
Hence Case 1 will have lesser acceleration because of lesser tension applied.