Two masses M 1 and M 2 are arranged as shown in the figure. Let ' a ' be the magnitude of the…

Two masses M1 and M2 are arranged as shown in the figure. Let 'a' be the magnitude of the acceleration of the mass M1. If the mass of M1 is doubled and that of M2 is halved, then the acceleration of the system is
(Treat all surfaces as smooth : masses of pulley and rope are negligible )

  1. M1+M24M1+M2a
  2. 2M1+M24M1+M2a
  3. M1+2M24M1+2M2a
  4. M1+2M2M1+M2a

Solution

Free body diagrams of M1 and M2 are shown below.

From the free body diagram of M2

M2gsinθ-T=M2a

And from the free body diagram of M1

T=M1a

Therefore,

a=M2gsinθM1+M2

When mass of M1 is doubled and mass of M2 is halved,

a'=M22gsinθ2M1+M22⇒a'=M2gsinθ4M1+M2=M1+M24M1+M2a

Asked in: AP EAMCET 2022 (04 Jul Shift 2)

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