Question

The two pulley arrangements shown in the figure are identical. The mass of the rope is negligible. In (1) the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (2). m is lifted up by pulling the other end of the rope with a constant downward force of 2mg. The ratio of accelerations in two cases will be

• A. 1 : 1
• B. 1 : 2
• C. 1 : 3
• D. 1 : 4

Answer 1

Answer: (C)

1 : 3

Answer 2

For first case $a _ { 1 } = \frac { m _ { 2 } - m _ { 1 } } { m _ { 1 } + m _ { 2 } } g = \frac { 2 m - m } { m + 2 m } = \frac { g } { 3 }$ …..(i)

For second case

from free body diagram of m

$m a _ { 2 } = T - m g$

$m a _ { 2 } = 2 m g - m g$ [As T= 2mg]

$a _ { 2 } = g$ ……..(ii)

From (i) and (ii) $\frac { a _ { 1 } } { a _ { 2 } } = \frac { g / 3 } { g } = 1 / 3$