Question

9.Find the acceleration of block of mass m. Assume pulleys are
massless and frictionless.
(A) g/3
(B) 2g/3
(C) g/2
(D) None of these
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Answer 1

Answer :

Let acceleration of block of mass 2m be a₁ and that for block of mass m be a₂$.$

Tension on 2m = 2T

Tension on m = T

Therefore, we can say that

• 2a₁ = a₂

Now from the FBD method, Net force on the block of mass 2m is given by

➝ 2mg - 2T = 2ma₁

➝ 2a₁ = 2g - 2T/m ...... (I)

Net force on the block of mass m :

➝ T = ma₂

➝ a₂ = T/m ...... (II)

Now, 2a₁ = a₂

⇒ 2g - 2T/m = T/m

⇒ 2g = 3T/m

⇒ T = 2mg/3

From equation (I)

⇒ 2a₁ = 2g - 2T/m

⇒ a₁ = 2g - 2(2mg/3m)

⇒ a₁ = 2g - 4g/3

⇒ a₁ = 2g/3

Hence, option (B) is the correct answer.