Question

Three smooth pulleys are connected by a light string. A mass m is attached to the pulley $P_3$. Assume the strings between two pulleys and between the pulley and the support to be vertical. If all the pulleys are massless then the tension in the string over the pulleys is

• A. 2mg
• B.
• C. Mg
• D. zero

Answer 1

The correct option is D

zero

Free body drawing of $P_1$

Applying second level

2T - T =$M_{P_1}$ $a_{P_1}$

as pulley is massless, $M_{P_1}$ = 0

$\therefore$ 2T - T = 0

$\Rightarrow$ T = 0

$\therefore$ Tension will be zero.

Be careful, you might assume that the system is in equilibrium and draw the free body of $P_3$ as

This will simply that 2T = mg which is wrong.

T=0, the mass will fall downwards freely.