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JEE Main 2025 (3 Apr, Shift 1) · Spring Systems

Spring Systems question from JEE Main 2025 (3 Apr, Shift 1)

Q36JEE Main 2025 · 3 APR · SHIFT 1Medium

Spring Systems

Figure

Two blocks of masses mm and M,(M>m)M, (M > m), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( μ=\mu = coefficient of friction between the two blocks) A. The time period of small oscillation of the two blocks is T=2π(m+M)kT = 2\pi\sqrt{\frac{(m+M)}{k}}

B. The acceleration of the blocks is a=−kxM+ma = -\frac{kx}{M+m} ( x=x = displacement of the blocks from the mean position)

C. The magnitude of the frictional force on the upper block is mμ∣x∣M+m\frac{m\mu|x|}{M+m}

D. The maximum amplitude of the upper block, if it does not slip, is μ(M+m)gk\frac{\mu(M+m)g}{k}

E. Maximum frictional force can be μ(M+m)g\mu(M+m)g.

Choose the correct answer from the options given below:

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Answer: (c)

  1. A: both blocks move together with mass M+mM+m: T=2πM+mkT = 2\pi\sqrt{\frac{M+m}{k}}. True.
  2. B: a=−kxM+ma = -\frac{kx}{M+m}. True.
  3. C: friction on mm is m∣a∣=mk∣x∣M+mm|a| = \frac{mk|x|}{M+m}, not mμ∣x∣M+m\frac{m\mu|x|}{M+m}. False.
  4. D: no slip needs mkAM+m≤μmg⇒Amax=μ(M+m)gk\frac{mkA}{M+m} \le \mu mg \Rightarrow A_{max} = \frac{\mu(M+m)g}{k}. True.
  5. E: maximum static friction on mm is μmg\mu mg, not μ(M+m)g\mu(M+m)g. False.
  6. So the answer is (c) A, B, D only.
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