Question

In the arrangement shown in figure, pulley 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,
(a) Tension in thread is 1/2 mg.
(b) Acceleration in pulley C is equal to g/2 downward.
(c) Acceleration of pulley A is equal to g/2 upward.
(d) Acceleration of pulley A is equal to 2g downward.
The correct answer is D!
Thanks in advance.

Answer 1

answer : option (D) acceleration of pulley A is equal to 2g (upward)

explanation : read this line which is mentioned in question, “pulley A and B are massless and the thread is inextensible”

means, pulley A and B can't apply a bit of force on thread. means, tension in thread is zero.so, without tension in thread, pulley C (which has mass m) fall downwards under gravity.

hence, acceleration of pulley C is acceleration due to gravity. i.e., $a_c$ = g (downward)

now from constraint rule,

$a_A=-2a_C$

i.e., acceleration of pulley A = -2g ( downward)

= 2g ( upward )

your last option should be -> acceleration of pulley A is equal to 2g (upward)

hence, option (D) is correct choice.