Want to Master Mass Pulley Spring System? Watch This IIT JEE 2019 Advanced Problem

Many students fail to solve the problems which deals with SHM and also some level of other concepts from mechanics are involved. I try to give the concepts here so that they find it relatively easier to solve such problems. Given that IIT JEE has been asking such questions for long time in the advanced exam.

The problems is as follows.

A block of mass 2M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a1, a2 and a3 as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is xo. Which of the following option(s) is/are correct? [g is the acceleration due to gravity. Neglect friction]

(A) xo = 4Mg/k
(B) When spring achieves an extension of xo/2 for the first time, the speed of the connected block is 3g√M/5k
(C) At an extension of xo/4 of the spring, the magnitude of acceleration of the block connected to the spring is 3g/10
(D) a2 - a1 = a1 - a3


To solve the problem, compute the absolute accelerations of the masses attached to the second pulley and then compute the tension in the string. Using this tension, write the F = ma equation for the spring mass system. Get the equation in the form of a SHM equation. Compute frequency, amplitude and time period of the motion. Then try to go over each options in the question and see if they are right.


Introduction: 0:00
Problem Explanation: 0:38
Pulley Concept: 1:50
Mass Pully F=ma: 2:30
Find Tension: 5:05
Sping Mass System: 8:15
SHM Concept: 10:20
Solving for answers: 12:00

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