Consider the infinite number of arrangement of pulleys as shown in the figure. A light string passes over each light and smooth pulley with one end to a block of mass m and connected to another pulley. The system is released from rest. The acceleration of the left most block is $\frac{g}{x} .$ Find the value of x.

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 2.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$m g - T = m a_{1}$

$m g - \frac{T}{2} = m a_{2}$

$m g - \frac{T}{4} = m a_{3}$

Constraint $T a_{1} + \frac{T}{2} a_{2} + \frac{T}{4} a_{3} + .......... = 0$

$a_{1} + \frac{a_{2}}{2} + \frac{a_{3}}{4} + ............ = 0$

$g - \frac{T}{m} + \frac{1}{2} (g - \frac{T}{2 m}) + \frac{1}{4} (g - \frac{T}{4 m}) + ....... = 0$

$T = \frac{3 m g}{2}$

$∴ a = - \frac{g}{2}, ∴ λ = 2$

Watch 3-min video & get full concept clarity