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Solution


Q.

Two blocks of masses m and 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 = coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is T=2π(m+M)k

(B) The acceleration of the blocks is a=kxM+m

       (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

(D) The maximum amplitude of the upper block, if it does not slip, is μ(M+m)gk

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

Choose the correct answer from the options given below:       [2025]
1 A, B, D Only  
2 B, C, D Only  
3 C, D, E Only  
4 A, B, C Only  

Ans.

(1)

A. Assuming no slipping, T=2πmtotalk=2πm+MkA is correct.

B. Let block is displaced by x in (+ve) direction so force on block will be in (–ve) direction

     F=–Kx ⇒ (M+m)a=–Kx

     ⇒ a=–Kx(M+m), B is correct.

C. As upper block is moving due to friction thus

     

     f=ma=mKx(M+m), C is not correct.

D. If both the blocks moves together at maximum amplitude, the friction force on the block of mass m is also maximum,

     For no slipping mkAm+M≤μmg

     ⇒ A=μ(M+m)gK, D is correct.

E. Maximum friction, fmax=μmg, E is incorrect.