First slide

Application of Newtons laws

Question

In the arrangement shown in the figure pulleys A and B are massless and the thread is inextensible. Mass of pulley C is equal to m. If friction in all the pulleys is negligible, then

Difficult

A

tension in thread is equal to (1/2) mg
B

acceleration of pulley C is equal to g/2 (downward)
C

acceleration of pulley A is equal to g (upward)
D

acceleration of pulley A is equal to 2g (upward)

Solution

FBD of C
$m g - 2 T = m c$ ……(i)
If we assume acceleration of A to be 'a'
upwards; by constraint equation we get:
$- a - a + c + a + c = 0 \Rightarrow a = 2 c$
and for block A:
$2 T = m_{A} \cdot a but as m_{A} = 0 \Rightarrow T = 0$
$so we get c = g and a = 2 g ↑$

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