InterviewSolution
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InterviewSolution
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A highly rigid cubical block (A) of small mass (M) and slide (L) is fixed rigidly on to another cubical block (B) of the same dimesions and of low modulus of rigidity (eta) such that the lower face of (A) completely covers the upper face of (B). The lower face of (B) is rigidly held on a horizontal surface. (A) small force (F) is applied perpendicular to one of the sides faces of (A). After the force is withdrawn, block (A) executes small oscillations the time period of which is given by.A. `(2 pi) sqrt(M eta L)`B. (2 pi) sqrt (M eta)/(L)`C. `(2 pi) sqrt (M L)/(eta)`D. `(2 pi)sqrt (M)/(eta L)` |
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Answer» Correct Answer - D When a force is applied on cubical block (A) in the horizontal direction then the lower block (B) will get distorted as shown by dotted lines and (A) will attain a new position (without distrotion as (A) is a rigid body) as shown by dotted lines. `eta = (F//A)/(Delta L//L) = (F)/(A) xx (L)/(Delta L) = (F)/(L^2) xx (L)/(Delta L) = (F) /(L xx Delta L)` rArr `F = eta L Delta L` `eta L` is a constant rArr Force `F prop Delta L` and directed towards the mean position, oscillation will be simple harmonic in nature. Here, `M omega^2 = eta L` `rArr omega = sqrt (eta L)/(M) rArr (2 pi)/(T) = sqrt(eta L)/(M) rArr T = 2 pi sqrt (M)/(eta L)`. |
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