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 a _

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Correct answer: C. a _ 2 - a _ 1 = a _ 1 - a _ 3

Using string constraint a _ 1 = a _ 2 + a _ 3 2 ⇒ 2 a _ 1 = a _ 2 + a _ 3 a _ 1 - a _ 3 = a _ 2 - a _ 1 ⇒ (C) is correct. for other options use m equivalent Equivalent mass Or Reduced mass m _ eq = 2 m _ 1 × m _ 2 m _ 1 + m _ 2 (for a two-mass system) = (2 (2m) × m)/(2m + m) = (4m)/(3) ⇒ T = ((4m)/(3)) . g ∴ 2T = 2 . (4mg)/(3) = ((8m)/(3))g ⇒ m _ eq = (8m)/(3) Using mechanical energy conservation ⇒ (1)/(2)k x _ 0 ^ 2 = (8mg)/(3) x _ 0 x _ 0 = (16mg)/(3k) ⇒ (A) is incorrect Option (B) ⇒ V _ x _ 0 2 = V _ = x _ 0 2 ω = x _ 0 2 (k)/(2m + (8m)/(3)) = x _ 0 2 (3k)/(14m) = g (32)/(21k) Option (D) ⇒ a _ x _ 0 4 = x _ 0 4 ω ^ 2 = x _ 0 4 (3k)/(14m) = 3k x _ 0 42m = (8g)/(21) For a simple harmonic motion x _ 0 ⇒ maximum displacement from extreme to extreme ⇒ x _ 0 = 2A ⇒ A = x _ 0 2 and ω = (k)/(m) = (3k)/(14m) ∴ v _ = A . ω and a = ω ^ 2 . x

A block of mass 2M is attached to a massless spring with...

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